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By Konstantinos Komnitsas, Evangelos Petrakis, Emmanouil Varouchakis

The paper discusses the limitations of population balance modeling (PBM) in predicting particle size distribution in grinding systems. It introduces a nonlinear framework that transforms the batch grinding equation into the Rosin-Rammler distribution, providing more accurate analysis under different operating conditions. The study uses marble as test material and investigates the adaptability of the nonlinear model with different media sizes.

Oct 1, 2023

By Mehmet Mesutoglu, Ihsan Ozkan

This study investigates the feasibility of rock bolting support in an underground coal mine gallery with a thick coal seam. The Ömerler underground coal mine working area, owned by West Lignite Enterprise of Turkish Coal Enterprises, was selected for this purpose. Longwall top coal caving is implemented as the production method in the Ömerler underground coal mine. Field and laboratory studies were conducted to determine rock mass and rock material properties, followed by experimental, empirical and numerical analyses based on the acquired data. The obtained design results were evaluated using a resin-grouted rebar rock bolting (RBR) system and steel arch support (SAS) pilot application areas. The numerical modeling results conducted using the fast Lagrangian analysis of the Continua 3D (FLAC 3D v6.0) program indicated less displacement and secondary stress change in the RBR-supported zone compared to the SAS-supported zone. In situ measurements also demonstrated that RBR provided more successful support to the roof during coal production activities. The findings suggest that RBR is a more effective solution when evaluating the feasibility of rock bolting support systems in underground galleries with thick coal seams at the Ömerler Mine. This study emphasizes the importance of more sustainable and safe support systems to enhance operational efficiency in the coal mining industry.

Mar 1, 2025

Improvements in cost efficiency, noise control, environmental design and ergonomics ? the mining and construction industries are facing demands on many fronts. The international manufacturers of construction machinery are responding to these challenges, and they will be presenting their innovations in all these fields at bauma 2013. bauma, the international trade fair for mining and construction machinery, mining vehicles, and building material machines, takes place from April 15 to 21, 2013 at the Messe Munchen exhibition center in Munich, Germany. The last bauma, in 2010, attracted 3,256 exhibitors from 53 countries, and more than 420,000 visitors from more than 200 nations. Covering a total of 555,000 m2 (5.97 million sq ft) of exhibition space, bauma is one of the largest trade shows in the world. This year?s fair is expected to surpass the 2010 figures. Here are some examples of the new developments visitors can expect to see at the show.

Jan 1, 2013

By Steve Kral

The Northwest Mining Association (NWMA) has been an advocate for the U.S. mining industry since 1895. For several decades, the organization has represented mining members located mostly in the Northwest and some southwestern Canadian provinces. Today, though, the NWMA?s membership is located in 42 states and seven provinces and has become a national voice for the mining industry. So, during the association?s 119th and final meeting as the NWMA, a name change was announced. The organization is now called the American Exploration and Mining Association (AEMA). But that?s not all that has changed, according to the association. The new name reflects more closely the diversity and location of the AEMA?s membership. It will still be an advocate for the mining industry, dealing with land, environmental and community issues on state and federal levels. The conference, held in December 2013 in Reno, NV, attracted about 2,500 attendees. And the accompanying exhibit included 230 equipment and service suppliers in 246 booths. Technical programming ran the gamut of mining industry issues and technologies, including surface and underground mining; high technology systems and automation in mining, metallurgy and exploration; along with social issues, finance and safety. The following is a sample of some of the sessions.

Mar 1, 2014

ShouSteel Mining Ltd., a subsidiary of ShouSteel (Group) Co., was founded in 1959 and is located in QianAn City in Hebei Province, China. ShouSteel?s pelletizing plant uses iron ore as a raw material combined with limestone, dolostone, or olivine, with bentonite as a binder. After mixing the raw materials and forming them into small, spherical balls, ShouSteel then fires pellets in kilns for hardening. The company sells the finished pellets as raw materials for blast furnaces used to produce industrial metals such as iron. ShouSteel?s handling capacity is approximately 24.5 Mt/a (27 million stpy) of ore. The company?s production capacity is 3.2 Mt/a (3.5 million stpy) of oxide pellets and 560 Mt (650 million st) of sinters. Until recently, ShouSteel Mining had not replaced its electronic scales in its series of ingredient chambers. Because of the wear and tear on these older scales, the weighing system began to encounter regular problems. The company experienced a high failure rate from the integrator, an unstable signal, weak anti-interference ability and low accuracy. ShouSteel also found that spare parts required during repairs were consistently high in cost and that system calibration was becoming increasingly frequent.

Jan 1, 2012

"With a longstanding reputation for engineering expertise, Weir Minerals continually develops solutions and technology to better serve the mining industry. Recognizing that throatbush wear rate has a major impact on the overall efficiency of slurry pumps, Weir Minerals has developed superior rotating and axial adjustment technology.In many applications, the pump’s throatbush is the component that has the shortest life compared to the impeller and liners, with considerable variability.Adjusting the gap between the throatbush and the impeller front shroud reduces hydraulic recirculation in the pump. This prevents localized wear on the throatbush, improves hydraulic efficiency and lowers the total ownership cost for the operator. To avoid impacting the plant’s production, these adjustments are often performed while the pump is operating. However, this can have safety implications for individuals working at the front of the pump unit.“Manually adjusting an alloy throatbush on a large pump requires several people and is laborintensive. It requires mechanical tools to adjust the four pusher bolts, one at a time, in order to reduce the gap between the throatbush and impeller. We wanted to find a safer and quicker way to extend the wear life of the pump with regular adjustments, which led us to development of this technology,” said Marcus Lane, global product manager for centrifugal pumps for Weir Minerals.“Our automated throatbush adjustment solutions are available for pumps fitted with either rubber or alloy throatbushes on Warman slurry pumps used in the most arduous applications, and have been designed with our customers’ safety and pump operation in mind. By mechanizing the adjustment procedure, personnel are removed from the line of fire, and the accuracy of axial movement is increased,” said Ron Bourgeois, director of slurry pumping technology group for Weir Minerals."

Mar 1, 2019

By Min Chen, Qinghua Liang, Weishan Yan, Yuan Feng, Shigang Wang

Various coal mine robots (CMRs) and unmanned aerial vehicles (UAVs) are implemented to explore unknown mines for improving the safety and efficiency of mining. It is challenging for CMRs and UAVs to achieve accurate positioning due to the absence of the Global Positioning System (GPS), poor lighting conditions, and similar geometric features in complex mine scenes. LiDAR-based localization and mapping methods are more accurate than others, while long-time running in large-scale scenarios will introduce nonnegligible cumulative errors. This study presents a semantic-aided Li- DAR simultaneous localization and mapping (SLAM) with loop closure, which leverages the uniqueness of mine intersection structure to establish stable semantic loop closure. Specifically, we propose a semantic intersection descriptor of translation and rotation invariance, which encodes 3D point clouds of the same intersection from different positions and viewpoints into a unified image. By using the semantic descriptor, we can construct a constant loop constraint when the same intersection is revisited from different directions to reduce cumulative drift. We provide experimental validation using large data sets collected in two large underground mines, namely, a simulated Edgar mine deployed in ROS Gazebo and a public underground mine data set provided by ETH. Experimental results show that the proposed method has higher localization accuracy and outperforms the existing LiDAR-based SLAM strategies.

Feb 1, 2024

By J. H. White

It is hypothesized that the Hotelling Valuation Principle (HVP) can determine the value of developed gold reserves using simple methods and easily obtained data. This paper reports the results of an empirical test of this hypothesis. Using publicly available data from North American gold companies, we obtained data for V, R, p, and c and ran a simple linear regression using equation (1.1) as the definition of the dependent and explanatory variables. By examining the value of the coefficients of the resulting regression equation, we can draw conclusion as to whether or not the HVP can be confident1y used as an estimator of the value of developed gold reserves.

Jan 1, 1995

By Shawn Benner, David Blowes, Carol Ptacek

A full-scale reactive barrier was installed into an aquifer impacted by acid mine drainage in August 1995 at the Nickel Rim mine site near Sudbury, Ontario. The primary mechanism of water quality improvement is bacterially mediated sulfate reduction and metal sulfide precipitation. Dramatic changes in the groundwater chemistry are observed with up to 90% decline in Fe (from >18 to <2 mmol L-1) and increases in alkalinity from <1 to >10 mmol L-1 (as CaCO3). Over a 3 year period, the rate of Fe removal declines by approximately 35%. Primary controls on barrier performance are organic carbon reactivity, groundwater temperature, and variable residence time within the barrier.

Jan 1, 2000

By Emily Wortman-Wunder

Attendees at December?s Arizona SME Section Conference at the Hilton El Conquistador Resort outside of Tucson, AZ were feeling optimistic and ready to get to work after a year of steady growth and recovery in the mining industry. During the two-day event (Dec. 5-6, 2010) and the preceding American Mining Hall of Fame banquet and awards ceremony, the focus was on copper, worldwide population growth and regulatory pressures, with several smart new projects featured alongside updates to traditional large-scale copper development projects. Keynote speaker Timothy Snider, chair of the University of Arizona?s Lowell Institute for Mineral Resources, hit the mood of cautious optimism when he analyzed the global demand for resources, using the case example of copper. Over the next 20 years, he said, the world?s population is expected to grow to 9.2 billion and the average annual per capita copper use is expected to rise from 2.2 to 4.5 kg (5 to 10 lb). The increase in demand will provide tremendous opportunity for mining companies, he said, but cautioned that the opportunities are balanced by negative influences on demand and pressures on supply. While demand for copper is currently growing, Snider noted that there were significant downward pressures on demand as well. These included a western world that is overbuilt, in-creasing use of substitute materials in new construction and the rise of wireless devices. He also noted new regulatory pressures, and pointed out that resource development now had to occur within a context of sustainability on several levels.

Jan 1, 2011

By S. J. Schatzel, K. M. Ajayi, E. N. Rubinstein, Z. Khademian

This study simulates the impact of a shale gas well casing breach near a longwall mine. Field studies are conducted to measure mining-induced permeability changes over the abutment pillar of a longwall mine, and a geomechanical model is developed in 3DEC, a three-dimensional numerical modeling code, to predict the aperture of fractures in the overburden at the study site. The predicted aperture values are used to determine mining-induced permeabilities, and the results are compared with the field measurements. These aperture values are provided as inputs into fracture flow code (FFC), which generates a stochastic discrete fracture network (DFN) model for the study site and predicts the potential shale gas flow to the mine. Results from 100 DFN realizations are statistically analyzed using the bootstrapping method to compensate for notable variation in fracture geometry. The results show a significant difference between the gas inflow for nearby panels due to increase in the induced permeability during mining of the second panel. The average gas flow to the mine was calculated as 4.72 × 10 m3/s (49 cfm) for a hypothetical breach at the Sewickley horizon during the first panel mining, 8.97 × 10 m3/s (19 cfm) for a hypothetical breach at the Uniontown horizon during the first panel mining, 2.16 × 10 m3/s (458 cfm) for a hypothetical breach at the Sewickley horizon during the second panel mining, and 8.07 × 10 m3/s (171 cfm) for a hypothetical breach at the Uniontown horizon during the second panel mining. Depending on the mine ventilation system, this could result in methane concentrations exceeding regulatory limits. Hence, these findings provide insights into the potential risk of an unconventional gas well casing breach near a longwall mine under shallow cover.

Feb 1, 2024

By William Gleason

"Despite the difficult economic climate for the mining industry, more than 6,300 people joined SME for its 2016 Annual Conference & Expo in Phoenix, AZ, Feb. 21-24.Nearly every commodity has been bruised and battered during the past year, leading to one of the more difficult cycles for the industry in the past decade. Coal has taken some of the hardest hits and other commodities, such as copper and iron ore, have felt the sting of a slower growth in China and an oversupply on the market.The difficult conditions could not be ignored, but they did not deter SME from offering a forum for the industry to share knowledge, network with peers and learn about the best products and practices while visiting the sold-out exhibit hall (844 booths and 627 vendors) or while attending any of the 121 technical sessions that were offered.The current state of the industry was one of the overriding themes of the conference and during the challenging times there are often cutbacks as operations look to become leaner and more efficient, however, there is one area that cannot be cut – health and safety.The conference kicked off with a fascinating presentation from Colonel Mike Mullane, a former NASA astronaut who, in 1978, was selected as a Mission Specialist Astronaut in the first group of space shuttle astronauts. He completed three space missions and logged 356 hours in space aboard the shuttles Discovery and Atlantis before retiring from NASA and the U.S. Air Force in 1990.In his speech to a packed audience, he warned of the dangers of cutting corners to get the job done more quickly by guarding against the “normalization of deviance.”Normalization of deviance is a long-term phenomenon in which individuals or teams repeatedly accept a lower standard of performance until that lower standard becomes the norm. Usually, the acceptance of the lower standard occurs because the individual or team is under pressure (budget, schedule, etc.) and perceives it will be too difficult to adhere to the original higher standard. Their intention may be to revert back to the higher standard when this period of pressure passes. However, by getting away with the deviation from the higher standard, it is likely they will do the same thing when the same stressful circumstances arise again. Over time, the individual/team fails to see their actions as deviant."

Apr 1, 2016

By J. C. Rhodes

The demand for good white minerals for many industries including paint and plastics have made it necessary to import high grade industrial minerals from various parts of the world. Some of the calcium carbonate, barite and talc minerals are from China, Mexico, Jamaica and Haiti. These materials can be processed by custom processors. The custom processor can provide a service to the Industrial Mineral owner. The imported materials can arrive in various feed sizes from lumps (3"-6") down to 325 mesh. The materials can also be in various size shipments or container loads. The economics for importing should be investigated thoroughly. The two factors just mentioned can influence the quantity of material to be processed. These two factors can also influence the total cost for each end product.

Jan 1, 1989

By Alden B. Carpenter

Brines (a solution containing more than 100,000 mg/l dissolved solids) in sedimentary basins are genetically related to evaporites in one of three ways: (1) dissolution of evaporite minerals, generally halite; (2) interstitial fluids in evaporites which are expelled from their source rock during compaction; (3) incongruent alteration of hydrous evaporite minerals (carnallite). Most brines of commercial interest originate as interstitial fluids in halite-rich rocks. These fluids are initially rich in magnesium, sulfate, and potassium but evolve in composition to an Na-Ca-Cl brine during their migration to their present host rock. A particularly important reaction in this process is: 2CaCO3 + Mgt+ = CaMg(CO3)2 + Cat (1a) This reaction reduces the magnesium content of the brine and ultimately converts it to a calcium-rich brine. The loss of sulfate occurs by two mechanisms. One of these is by direct precipitation as calcium sulfate (either as gypsum or anhydrite): Ca 2+ + SO4 2- = CaSO4 (2a) Additional sulfate may be lost from the brine by sulfate reduction: S042 + 1.33CH2 + 214- = H2S + 1.33CO2 + 1.33H20 (3a) The loss of carbonate species occurs by precipitation as carbonates: H2O + C02 + Cat = CaCO3 + 2H+ (4a) The net result of reactions 3 and 4 is: Ca 2+ + SO4 2- + 1.33CH2 = H2S + CaCO3 + 0.33H2O + 0.33CO2 (5a) The loss of potassium from brines is caused by the formation of potassium aluminosilicates: 2K+ + Al2Si2O5 (OH)4 + 4SiO2 = 2H + 2KAlSi2O8 + H2O (6a) The hydrogen ions produced by this reaction dissolve carbonates: 2H+ + CaCO3 = Ca 2+ + CO2 + H2O (7a) The net result of reactions 6 and 7 is: 2K+ + CaCO3 + Al2Si205 OH)4 + 4SiO2 = Ca2 + 2KA1Si3O8 + H2O + C02 (8a) A study of brines from central Mississippi has shown that the composition of these brines is related to the interaction of pore fluids from evaporites with minerals in the enclosing sedimentary rocks.

Jan 1, 1978

By Ted D. Johnson

INTRODUCTION The tailing dam is part of the SOHIO L-Bar Uranium Mine and Mill located about 70.8 kilometers (44 miles) west of Albuquerque in northwestern New Mexico. The dam location is shown on Figure 1. The tailing dam is one of the last upstream method dams permitted in the industry. Design and construction aspects of the project, as well as operation and maintenance considerations, are reviewed herein. Since initial construction, SOHIO Western Mining Company and Woodward-Clyde Consultants have developed several modifications and improvements in the dam&apos;s operating and monitoring procedures. This work has been done in coordination with the New Mexico State Engineer&apos;s Office and in accordance with recommendations in a report done for the Corps of Engineer&apos;s Phase I Dam Inspection Report. Modifications and improvements described should be of particular interest to owners and operators of other tailing dams utilizing the upstream method of deposition. The tailing facility was designed for a 10-year life to provide an ultimate storage capacity of 6 1/2 billion kilograms (7 1/2 million short tons) in an area of about 180 acres. A plan view of the tailing dam is shown on Figure 2. The tailing consists of approximately 75% sand size material and 25% fines (material passing the No. 200 sieve). The tailing dam includes a small earth starter dam with raises of the dam accomplished using tailing deposited by upstream method techniques. The starter dam is a homogeneous embankment about 610 meters (2000 feet) long, a maximum height of 12 meters (40 feet) and 2 1/2:1 (horizontal to vertical) upstream and downstream slopes. The starter dam contains an internal drainage system which includes a near vertical chimney drain connected to horizontal finger drains. A typical section through the maximum height of the starter dam is shown on Figure 3. A small confining dam, approximately 1.6 meters (5 feet) high, is constructed beyond the limits

Jan 1, 1980

By K. C. Ko, M. D. Bunnell

The studied coal mi1e is an underground coal mine located in the northern Wasatch Plateau of central Utah (Figure 1) . Since operation began in 1981, in situ stress conditions have been encountered which differ from the assumed conditions utilized during early mine design efforts. Geologic structures also varied somewhat from those projected during initial geologic interpretations of the area. The encountered geologic conditions combined with the unusual stress conditions prompted a combined study of in situ stress and stress-related geologic structures. The study was conducted in two phases, with phase 1 consisting of detailed underground mapping and analysis of stress-related geologic structures to determine stress orientations from which they originated; and phase 2, consisting of over- coring two sites within the mine to determine present in situ stress orientations and magnitudes. GEOLOGIC ANALYSIS Three types of geologic structures have been encountered in the mine that act as indicators of stress orientations of the geologic past. Two of these structures, faulting, and igneous dikes, are directly measurable in the mine. A third type of structure, photolineation, was detected through remote sensing methods and shoe god correlation to roof conditions in certain areas of the mine. Faults Two major orientations of faulting have been encountered in the studied coal mine, including a system of N 80 W striking normal faults and a system of N 55 to 70 W striking oblique-slip faults. Only data collected from the oblique-slip faults were used for this study due to the fact that these faults offset the N 80 W faults wherever the two systems intersect, indicating that the N 55 to 70 W system was created by a more recent stress field. Figure 2 shows locations within the mine where data were collected from seven locations along oblique-slip faults. Data collection consisted of measurement of fault plane strike and dip, fault slickenside trend and plunge, and slip direction. The data are tabulated in Table 1. The fault data were then plotted on stereo nets to determine the stress orientations present at the td of faulting (Figure 3). The determined stress orientations are 32~0 included in Table 1. The stereo net plots show average principal stress orientations of: 1) [ ] plunge 1 degree. These data suggest that the N 55 to 70 W oblique-slip faults were produced by a nearly

Jan 1, 1986

By John L. Stauffer, Allan Lipton, Kim Leitzel, Lesley Gaydos, Laurence M. Demers, Douglas C. Kuhn

Eicosanoids and cytokines produced by the alveolar macrophage (AM) are key mediators of pulmonary inflammation and fibrosis resulting from occupational exposure to mineral dust. In order to determine if eicosanoid and cytokine production are altered by chronic inhalation of coal dust, we compared the production of prostaglandin E2 (PGE2), thromboxane A2 (TxA2), leukotriene B4 (LTB4), interleukin 1 (IL-1), tumor necrosis factor (TNF) and platelet-derived growth factor (PDGF) by cultured AM from non-smoking normal human volunteers and coal miners. Inhibitors of eicosanoid biosynthesis were administered to AM from coal miners in order to determine if a link between eicosanoid and cytokine production exists in these cells. Basal PGE2, TxA2, TNF and IL-1 production by AM from active miners was increased compared to AM from normal volunteers. However, the production of these eicosanoids and cytokines by AM from former coal miners was reduced compared to control AM. Administration of the cyclooxygenase inhibitor, suprofen, and the lipoxygenase inhibitor, nordihydroguaiaretic acid, reduced PGE2 and TxA2 production in miners&apos; AM but had no effect on LTB4, IL-1 or PDGF production. Specific inhibition of thromboxane synthase by UK38,485 was associated with a significant reduction in TNF production in active miners&apos; AM but had no effect on PGE2, LTB4 or IL-1 production. The prostacyclin analogue ZK96,480 also specifically inhibited TxA2 production in active miners&apos; AM. The results of these studies suggest that coal dust exposure is associated with alterations in AM eicosanoid and cytokine production which may be relevant to the development of pulmonary inflammation and fibrosis. In addition, the lack of effect of inhibitors of PGE2 biosynthesis on IL1 production in miners&apos; AM suggests the production of these intercellular messengers may not be linked in AM chronically exposed to coal dust.

Jan 1, 1991

By Erica Frederickson

"Millennials. Doesn’t the word just make your blood boil? You’ve probably encountered one of those kids who think they know best despite a lack of any real experience.Hi, my name is Erica, and I am a Millennial. We often get a bad rap, sometimes for good reason. But we do have qualities that are often overlooked. For example, I am happy to share with my generation a real desire to make a difference in the world and a commitment to innovation. Does this mean I think we always have good ideas? No – especially not right away. After all, few of us came anywhere near a piece of construction equipment until arriving for our first job, as was the case for me. We may have fancy degrees, but not many of us learned to run a jackleg drill in school.Two weeks after graduating college in 2011, I packed up my bags and moved to New York City to work as a field engineer for Traylor Bros. Inc. on the Queens Bored Tunnels project (Granite/Traylor /Frontier Kemper, JV), part of NYC MTA’s multi-billion dollar Long Island Railroad East Side Access project. It was here I became acquainted with the notorious New York City union workers. Perhaps the greatest challenge of my career thus far was earning the respect of the field supervision and craft workers on this first project.The first time I asked a maintenance mechanic to clean a piece of equipment in accordance with our maintenance protocol I got a flat-out “No.” It was the most powerless I had ever felt. But why should these experienced workers trust a 21-year-old girl with her civil engineering degree and no prior experience? I realized no employee on the job had any reason to listen to me — not until I proved my worth. Fortunately, I arrived on the job site just as we were commissioning the slurry plant for the first tunnel drive. I dove into learning as much about the slurry tunneling process as possible and was able to quickly pick up the ins and outs of running the slurry separation plant. As none of the other engineers or management had first-hand experience on a slurry tunneling job, I soon became the go-to engineer in the slurry plant. No one questioned me if I asked to have something done around the plant after that, or if they did, they quickly learned that I had a convincing answer as to the need for the task. I was even able to play a large role in shaping our slurry monitoring and control methodology."

Jan 1, 2015

By William Gleason

The evolution of technology has made the world a more connected place. It continues to change the way we power our homes and vehicles and is leading to a future that seems to be limitless. Limitless as long as we can continue to supply the minerals necessary for technology to produce better iPhones, more efficient electric cars, better wind turbines and sophisticated national defense systems. These minerals, dubbed critical minerals, have surged in importance in every corner of the world and, on Aug. 3-4, they were topic of conversation at the Critical Minerals 2014 conference in Denver, CO. The conference, hosted by SME and the Australasian Institute of Mining and Metallurgy (AusIMM), looked at critical minerals from every angle, from where they are found to what the future might be. Among the minerals that have been called critical are rare earths, a collection of 17 minerals that have become increasingly important as technology continues to advance in everything from communications to energy to national defense. Leading off the conference, David Abraham, senior fellow at the Institute for Analysis of Global Security, explained that, like many people, he is relatively new to rare earths. Unlike most people, though, Abraham developed more than a passing interest in the minerals and has since travelled the world to understand the role of rare earths ? where they are found, how they are mined, how they get to market and, eventually, what applications they are used in. Following his travels, he said he returned concerned about the sector and how the industry will keep up with the demand that only seems to be growing in the modern world. And, Abraham noted, that it is not just the developed world that is driving demand. It stretches even to places like Indonesia, where the average annual income is about $3,000/year. Yet, the nation is one of the most active places in the world for social media with a population that is wired in with all kinds of electronics. The problem facing the sector is, and has been for a long time, and especially since 2010, supply of the minerals. At one time, China produced about 98 percent of the world?s supply and controlled the sector completely. In 2010, as the world began to demand more rare earths and develop other sources, China announced an export ban on rare earths. This changed the game completely, from the production lines all the way to the floor of the U.S. Congress.

By J. A. Finch

The photographic measurement of bubble diameter is tedious and restricted to vessels with transparent walls and relatively low bubble concentrations. A new method for predicting bubble diameter in a flotation column has been developed and confirmed by comparison with measured mean bubble diameter (Yianatos et al., 1987) Flotation columns are not mechanically agitated. This note describes an extension of Ms method to a mechanically agitated flotation machine. A recent publication by Szatkowski (1987) provided sufficient data to calculate bubble diameter by the proposed method and compare with values determined photo- graphically. Method In a two-phase system (gas and liquid), bubble diameter (db), superficial gas rate (Vg) and liquid rate (Vl), and gas holdup (Eg) are linked by two relationships (see the nomenclature at the end of the paper for definitions of symbols). [ ] Equation 1 is the definition of slip velocity (relative gas to liquid velocity) for a countercurrent gas-liquid system, and equation 2 is an adaptation (Yianatos et al., 1987) of the expression of Masliyah (1979) for hindered settling in a multispecies system. The solution for bubble diameter is by repetitive substitution of estimates of db in equation 2 until the calculated Ubs is equal to the measured Ubs in equation 1. Results and discussion Table 1 presents the data obtained by Szatkowski (1987) from a mechanically agitated laboratory flotation machine. The machine generated bubbles by directing a gas stream into the vicinity of a disk rotating at Ngh speed (up to 8000 rpm) in the flotation slurry. The air was completely dispersed in a swarm of fine bubbles. A photographic technique was used to determine the distribution of bubble size. The mean diameter and standard deviation were then calculated. Table 1 provides all the information necessary for computing bubble diameter (Vl is assumed zero). The calculated bubble diameter is presented in Table 1 as d;. Figure 1 plots measured versus calculated bubble diameter and shows reasonable agreement between values. There is an apparent tendency to undercalculate the small bubbles and overcalculate the large ones.

Jan 1, 1987