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By Stephen W. Lambert

One of the primary interests of the United States Department of Energy's Mine Planning Division is to fully develop avenues of technical research which potentially offer positive effects on coal mine productivity. One such area of research involves the removal of methane gas from unmined portions of coalbeds through vertical wells drilled from surface locations. As coalbed methane content is reduced, less gas is available for flow into the mine, and consequently ventilation requirements are decreased and/or coal extraction rates increase. Another attractive aspect of the vertical borehole drainage method is that it presents an opportunity to recover and utilize significant quantities of methane gas, which would otherwise be wasted to the atmosphere. The viability of removing gas from the Mary Lee coalbed using stimulated vertical boreholes was first suggested by Elder and Deul as a result of a United States Bureau of Mines' drilling project conducted from 1971 to 1974 (4). Other United States Bureau of Mines' studies forecasted that degasification would eventually be necessary in the Mary Lee coalbed because most new or expanding mine development would take place at depths exceeding 1 000 feet (305 meters), where the methane problem would be severe (3) (13). In 1975 a large-scaled drilling program was designed in order to supply industry's anticipated need for a degasification technology in the Warrior coal basin, Alabama. The results of this government/industry sponsored effort were to be specifically applicable to the Mary Lee coalbed, the most extensive and economically important deep minable coal present in the area. Major technical objectives of this program are twofold: (1) to measure the effects of various well completion designs, particularly hydraulic stimulation, on mining and (2) to determine the effects of well spacing on gas drainage rates. A cooperative agreement was established with United States Steel Corporation in late 1975 and field work began shortly thereafter in the proximity of a newly developing mine near Oak Grove, Alabama. Government responsibility for this program was transferred from the United States Bureau of Mines to the United States Department of Energy in October 1977. To date, as a result of this program, twenty-one wells have been completed into the Mary Lee coalbed at the Oak Grove site. Seventeen of these wells were drilled on an experimental grid pattern located two miles from the active mine. These grid wells are primarily being used to generate data necessary to determine the effects of well spacing on gas drainage rates and will also provide a large amount of information regarding the long-term effects of degasification on mining. The four remaining wells (designated Ton through TW4) were placed near the mine so that the full effects of completion could be studied within the short time required for underground interception. Results gathered from the first two test wells (TW1 and TW2) have been reported in detail (10) and indicated that several improvements were necessary to increase gas drainage rates. Hydraulic stimulation was one of the most important aspects of well design that required improvement. Nitrogen-charged foam stimulation treatment was used at TW3 and TW4 instead of the gelled-fluid type stimulation used at the first two near-mine test wells.

Jan 1, 1980

By Leo Misagi

THE ROLE OF MANAGEMENT IN PLANT SAFETY Safe Production In plant management, safe production is an ideal. It becomes reality when: 1. Plant employees work in healthful and safe conditions. 2. Plant safety is in harmony with productivity. 3. Worker absenteeism and turnover are low-the work force is stable. Plant management must apply its talents, skills, and resources to build and maintain the foundations of safe production on a system of policies, procedures, and attitudes. It must do so by marshaling all managerial functions - staffing, direction, control, innovation, and representation-toward that goal. Ideally, a plant safety program is proactive. Management should plan and implement safety activities that are aimed at prevention. Past accidents-accomplished facts-should not be the sole guide of future actions. In other words, positive preventive measures, not the fewness of accidents are the criteria for safety production. An ideal safety program is one which is cost effective. Management should view plant safety as part of a broader program-loss control. Loss control includes prevention of fires and other accidents, unhealthful conditions, and occurrences that cause bodily injury, illness, property loss, or damage. Management evaluates the employees' productivity and safety. An effective training program aimed at loss control is the hallmark of safe production. Ideally, both labor and management should be well versed in safety. They believe in the premise that work-related injury and illness, as well as property loss and damage from fire and other accidents, are manageable and preventable. Such belief prompts them to learn more about the work process and potential hazards associated with each job. They also learn how to expect and prevent fues and other accidents, and respond to emergencies at the plant. Plant management determines which individuals or groups of employees are accountable for the following functions:

Jan 1, 1991

By Andrzej Wala

Constantly increasing demand for energy materials and metal ores brought about tremendous progress in mining techniques which are characterised by a high degree of mechanization and concentration of works. One of the recent trends in underground mining mechanization is connected with an application of heavy machines with diesel engines [l],[2]. The introduction of diesel engines in mining all over world caused not only improvement in economic conditions but also the necessity to prevent contamination of air in the mine by toxic agents in diesel exhaust emissions. A generally used way of eliminating exhaust gases is proper ventilation of the cross cut by means of providing permanent exchange of air that would guarantee in every point of the cross cut and in every moment the decay in concentration of exhaust gases beyond threshold limit [3][4][5][6][7][8][9][10]. The present paper is an attempt to define a mathematical model describing the changes of concentration in cross cut face to which fresh air is distributed by ventilators and tubes in a forcing way. Obtained model should offer its practical adaptability to engineering calculation of the amount of fresh air needed for diluting and eliminating exhaust gases beyond threshold limit. Justness of these models has been confirmed by investigation of the growth of nitrogen dioxide concentration in air environment in some cross cut faces of Kiirunavaara iron ore mine in Kiruna (Sweden).

Jan 1, 1980

By Marcel Haffen, Jean Janin

The purpose of grouting is to modify the permeability and strength characteristics of the subsoil in such a way that the planned structure can be efficiently constructed at a given location. This technique, which originally underwent considerable development in the field of dams construction is constantly evolving and it becomes more and more important in urban zones of intensive underground development for projects such as transport tunnels, stations, car parks, ect. Grouting becomes more and more indispensable whatever the natural characteristics of that subsoil ; such is the case particularly when the planned work runs through cohesionless granular soils, usually water-bearing such as alluvium, sands, disturbed ground, fill material, etc. The selection of the grouting method and the extent of treatment required at depends on two fundamental factors. 1º) nature and behaviour of subsoil to be treated. There is no need to stress the necessary of a good knowledge of geotechnical, hydrological and chemical characteristics of the ground to be treated. At the present time the specialists in these fields have available numerous methods of analysis, either laboratory or field tests, which enable to evolve a suitable treatment.

Jan 1, 1997

By Robert A. Jankowski, Charles A. Babbitt, Natesa I. Jayaraman

Today, approximately 31% of underground coal mining operations have designated occupations or areas with more stringent (below 2.0 mg/m3) respirable dust standards in place. Many U.S. coal mines have been able to maintain compliance with very low dust levels, and the Bureau of Mines, in an effort to identify those factors contributing to low dust levels, completed a survey of twelve continuous miner sections which were able to maintain their dust levels at or below 0.5 mg/m3. The quantity and quality of face ventilation appeared to be the most important factor in controlling dust exposure. The results directed Bureau research towards identifying improved face ventilation techniques for reducing quartz dust levels on continuous mining operations. This research has involved the evaluation of a half-curtain face ventilation technique which reduces the cross-sectional area of the entry, thus increasing the air velocity over the operator. The Bureau has also conducted extensive laboratory studies to compare tubing versus brattice, including an evaluation of both systems in a crosscut turn. In an effort to improve ventilation and reduce dust exposures of roof bolter operators working downwind of the continuous mining machine, the Bureau has evaluated two novel face ventilation systems. The first system consists of a fan discharge tubing technique which routes dusty air away from the return entry being bolted. In a technique similar to the fan/tubing concept, exhaust air from the upwind continuous miner face can be scrubbed using a dust collector to capture a portion of the dusty air, clean it, and supply it to the bolter operators as a split of clean intake air. A better understanding of face ventilation techniques should lead to solutions to the problem of more stringent dust standards due to quartz.

Jan 1, 1989

By S. Frimpong

The coal mining industry is an important sector of Canada?s economy. The cost of mining and haulage of coal in Western Canada is a major focal point when compared to inexpensive coal from Australia. Spot coal price volatility affect contractual price arrangements and this creates pressure on companies? profit margins and their competitive edge. In order to alleviate this pressure, companies may have to take short-term drastic measures that may hurt their strategic positions in the long-term. Companies must also create a mix of their products to ensure effective maintenance of profit margins given various quantity and quality constraints. In this paper the authors provide extensive analysis based on detailed probabilistic production systems for coal extraction and haulage in Western Canada. An optimization model is formulated for typical coal mining operations, processing and haulage from mine sites to the Vancouver Ports using linear programming algorithm. A stochastic model is also formulated to analyze the associated risks and uncertainties. These models are validated using data from five operating mines in Western Canada with varying quantity and quality products and uncertainties. The results show that the five mines studied have to produce between 180,000 and 2.10 million tonnes of metallurgical coal and between 70,000 and 2.16 million tonnes of thermal coal to enhance their profitability given the underlying constraints. The average expected probability of success associated with production capacities from these mines is about 66%. This results in a failure probability of 36%, which is extremely high under contractual arrangements. The results also show that management?s profit expectation of $83 million can be achieved at a zero percent failure probability. With a higher risk of failure of 10%, this expectation increases by 21% to $100.3 million.

Jan 1, 2011

By Jacek Kolacz, Knut Lyng Sandvik

Fine grinding in an air swept and a grate discharge ball mill working in closed circuit with a forced vortex air classifier has been investigated in continuous laboratory scale. Minerals with different physical properties were ground down to 40, 20, and 10 micron top size. The shape of the product particle size distribution curve was investigated and specific surface (BET) was measured. During production of material with top size of 40 microns in an air swept mill, the capacity was up to 25% higher when compared to a grate discharge mill. This difference dropped to 180A during production of 10 micron top size material. A corresponding decrease in power consumption was observed. An important finding is that by regulation of the air flow rate through the mill, it is possible to achieve products with different specific surfaces and particle size distribution curve steepness. During production of the 10 pm material, the specific surface could be varied in the range 3 to 4.5 m2/g. Such powders could hardly be produced in a grate discharge mill because fine particles coated the grinding media and the lining. On the other hand the internal classification in the air swept mill kept the size distribution of the mill content relatively free of fines. This prevented a similar slowing-down of the air swept grinding process.

Jan 1, 1995

By Thomas E. Finch

Coal produced from surface mines in the Western United States is becoming a more important part of this nation's economy as other types of fuels become scarce. This paper reports the investigation of alternative methods of handling the parting between two coal seams. The results of this investigation are presented as the engineering-economic aspects of alternative parting handling methods involving stowing or back filling techniques. The coal and parting characteristics were selected as being representative of those under consideration or actively mined in the West. The basic philosophy of evaluation is to establish a mine-within-a-mine where equipment selected for minimal capital investment can remove the parting and second seam nearly independent of the ongoing, present production. With proper consideration of design, this parting-coal removal is evaluated as a second operation within the first and has its own profitability measure. The Fort Union Area of Montana, Wyoming, and the Dakotas contains large reserves of low sulfur sub-bituminous coal. In many locations, several coal seams are close to the surface and are separated by relatively thin layers of parting. The removal of overburden and the mining of the upper seam is accomplished effectively with conventional mining methods and equipment. Mining a second seam of coal and handling the parting in accord with economic and environmental controls presents a number of problems. Typically, mining companies have adapted the conventional strip mining techniques used in the East. However, the extreme thickness of the western coal seams offers alternative mining method possibilities for parting and second seam removal.

Jan 1, 1976

By Larry Powell

Rend Lake is an Army Corps of Engineers reservoir located in Franklin and Jefferson Counties in south-central Illinois. The lake consists of 20,000 acres of water and 19,000 acres of public access land. The site attracts over two million visitors a year and is surrounded by campgrounds and other recreational facilities. The lake overlies the largest tonnage of low sulfur coal in the state. Coal is being removed beneath the lake from five mines operated by three coal companies. Currently high extraction mining operations are approaching low-lying, environmentally sensitive, and high-use recreational areas. Advanced planning to maximize coal extraction and minimize potential effects of subsidence requires the development of procedures to assess the impact of high-extraction mining on the land use of the area. The Bureau of Mines, the Corps of Engineers, and the coal companies have initiated research to assess the following proposed planning steps to ensure the maximum recovery of the coal resources while minimizing impacts to surface land use: 1) Establish a dialogue between the surface and mineral owners; 2) develop a geographic information system to aid in assessing existing land use and potential changes; 3) assess the potential effects of subsidence on drainage, wildlife habitats, and changes in land use prior to mining; 4) coordinate the mining displacements with surface activities to minimize disruption; and 5) develop appropriate mitigation plans before mining occurs.

Jan 1, 1986

By C. E. Jordan

The Bureau of Mines conducted research to measure the improvement provided by fine bubbles on the flotation of fine-sized particles (minus 20-um size) in an effort to improve flotation efficiency in our domestic minerals industry. The turbulent velocity distributions of the fluid within the flotation cell were measured as a function of time and position and used to increase the precision of a fine particle, turbulent flotation model. For the mineral system investigated, improved flotation response was obtained under laboratory conditions by using small bubbles and intense agitation. These results matched the model's predicted response.

Jan 1, 1989

By M. C. Stuttle

MDL Rock Lasers has undertaken successful mapping trials of abandoned mine workings using its underground cavity scanning system. The work was being performed for Kalgoorlie Consolidated Gold Mines (KCGM), Australia's largest gold producer. MDL Rock Lasers supplies underground surveying systems to the mining and quarrying industry KCGM's Fimiston Super Pit, located in Kalgoorlie, Western Australia, is Australia's largest open-pit gold operation. Fimiston's final pit design is expected to be 3.7 km (2.3 miles) long, 1.5 km (0.9-miles ) wide and 540 m (1,770 ft) deep. During the early days of Australian mining, underground operations were labor intensive. Mining was selective and generally narrow stopes were mostly backfilled. Improved processing technology and mine mechanization during the 1970s and 1980s has permitted larger scale operations to adopt less selective underground-stope operations. The "super pit" concept was a logical step for mining companies working toward economies of scale. However, the industry recognized that there was no precedent for excavating a 500-m- (1,640-ft-) deep open pit through ground previously affected by old workings. To appreciate the geotechnical challenge facing KCGM, it is necessary to consider that under the pro¬posed area at the open pit, stoping reached a level of 1 km (0.6 miles) and was supported by more than 2,000 km (1,240 miles) of development headings. The company was fortunate because plans were available for the Golden Mile underground operations. The existing plans were interpreted by the mine's geotechnical team and computer models were constructed of the underground workings. These models can be imported into three-dimensional mine planning packages, such as the Vulcan's Unix-based software, Envisage, to assist analysis and design. This prior knowledge of the workings provided the focus for investigating and confirming ground conditions using probe drilling. After several iterations of drilling, followed by detailed analysis, several decisions were made relating to the nature of the ground and the mining approach to be taken. It was recognized that the stope models were not perfect due to hu¬man error, lack of original survey information and progressive deterioration in ground conditions. It also became apparent that the sole reliance on probe drilling was inefficient in terms of time and quality of information. This was particularly true in complex areas where stopes are in close proximity. A major concern was the presence of open stopes (voids). In many cases, stopes consist of combinations of filled and void sections. The condition of pillars within these underground workings is extremely important. In time, pillars collapse and voids will propagate in upward and lateral directions. So systems needed to be developed that allowed rapid and accurate verification of ground conditions. KCGM was introduced to MDL Rock Lasers while investigating technology for underground mining. The two companies decided to use the C-ALS, MDL Rock Laser's underground laser, cavity scanning system, to improve the management of mining through affected ground. This system was to be used in conjunction with probe drilling and void mapping activities. A field test in one area of the Fimiston Mine verified the capability of the C-ALS system to quickly and efficiently assist in this decision making process. The C-ALS scanner features lightweight, carbon fi¬ber alignment rods from Measurement Devices Ltd.'s (MDL) Boretrak MKII. This is a borehole deviation system that stops the two axis measurement head rotating and lowers the system down a borehole. The scanner is deployed by a 110-mm (4.3-in.) borehole, up, down or sideways. The operator can then carry out vertical and horizontal plan section scans at any user specified ARC (an angular increment of 2°) or the distance between two points on the ARC (CHORD) increments. Windows '95 software enables the operator to control the cavity scanner remotely, surveying the area in real time. The system makes data quick and convenient.

Jan 1, 1999

By G. Fehr, B. B. Panda, R. Bansberg, K. Arnold, T. Freiman

To evaluate the potential for process solutions to contaminate groundwater outside of the area of the Oxide Pit, it is necessary to predict the ultimate maximum pit lake elevation once pit-related mining activities have ceased. A water balance model was developed based on the existing pit geometry, the groundwater flow equation, and assumed hydrologic input parameters. The model assumed that at any point in time, total inflow into the system (i.e., direct precipitation, surface water and groundwater) minus outflow from the system (evaporation from the lake surface) was equal to the change in the pit water volume. The pit lake depth over time was predicted by assuming a succession of steady- state water balance conditions over short time increments. An analytical method using a spreadsheet and computer model was employed in this study to model the filling of the lake in the Oxide Pit. A sensitivity analysis was performed to evaluate uncertainty associated with the input parameters in the model. The sensitivity analysis indicated that the model was most sensitive to values of precipitation and evaporation and to the static water table.

Jan 1, 2003

By C. J. Hall

An investigation of multi-shaft airflow problems by the author in 1976 (1) was presented in the hope of arousing considerable written comment, but in fact-. only one contribution (2) was forthcoming. The investigation in this paper is taken several stages fur¬ther, because the matter is of major importance in many American hard rock mines with complex networks extending over thousands of meters vertically. The examples used have all been generated thermodynamical¬ly and checked by motive column (denisty) calculations. Dry air has been used to reduce the amount of time spent on the rather complex calculations, but it has been shown (3) that the principals developed apply equally well to air/vapor/water mixtures. Initially the subject is investigated using both thermodynamic and motive column analyses. The latter part of the paper concentrates on a motive column presentation. Both methods are, of course, equally valid and give identical answers to any situation when correctly applied, as is shown in the worked examples.

Jan 1, 1980

By Bern Klein, Richard W. Lawrence, Scott Frostad

A laboratory study was conducted to evaluate the effects of various kinetic test protocols on sulfate production, NP depletion and time to acidity. Six test protocols were evaluated including standard humidity cells, non-aerated cells, tall cells, shaken cells, simulated precipitation cells, and NP depletion columns. The study indicates that test protocols which disrupt the oxidizing environment, such as extreme wetting and drying cycles, shaking the cells, or the high addition of acidic water will create an unnatural environment that affect the results. Trickle leach and non-aerated test protocols create an oxidizing environment that more closely represents field conditions and are therefore recommended.

Jan 1, 2000

By Y. H. Alghamdi, A. D. S. Gillies

"INTRODUCTION Background Diesel Particulate Matter (DPM) has been a critical issue during the last decade in underground mines. This problem is threatening the health of mine workers, as well as the mine’s productivity. It has been confirmed that the diesel engine exhaust is the main source for the diesel particulate matter (DPM), and that it has the highest impact in raising carbon monoxide, carbon dioxide, oxide of nitrogen, and hydrocarbons in the underground environment. Miners who are exposed to this kind of emission are at high risk for developing lung cancer and other lung diseases. The Mine Safety and Health Administration (MSHA) has issued standard rules to regulate diesel emissions in underground mines. The final ruling confirmed in 2008 that the total carbon should not exceed 160 µg/m3. (MISHA, 2008) Monitoring DPM in underground mines has become important to ensure compliance with the MSHA regulations. There are many different types of DPM monitoring systems that are currently being used in underground mines. Two methods are typically used for DPM sampling: the personal sampling method or the direct exhaust sampling method, which takes a direct sample from the engine’s tailpipe. Many mines do not recommend using the direct exhaust sampling method since it involves complex measuring equipment and procedures, as well as it is not regulated in the United States or Canada. Thus, the personal sampling method is the preferred method in many mines when taking DPM samples. Even this method includes many variations, such as the Respirable Combustible Dust (RCD) method and the method devolved by the National Institute for Occupational Health and Safety NIOSH 5040. The NIOSH 5040 method is the preferred method overall because it gives more accurate measurements compared to the other methods. This method does not allow organic carbon sources other than those coming from diesel engine exhausts to interfere with the measurements, which otherwise would lead to overestimating the actual amount of the DPM in the mine environment. An impactor feature in the cassette, which holds the samples in the instrument, characterizes this method. Since the diesel particles are less than 0.9 micron, this impactor does not allow particles more than 0.9 microns to be collected in the cassette filter. The cassette is then analyzed in a lab and the concentrations of organic carbon (OC), elemental carbon (EC), and total carbon (TC) are determined. Lately, the National Institute for Occupational Safety and Health (NIOSH) has developed a new instrument that can use the same concept of NIOSH 5040, but with instant measurements of elemental carbon. It utilizes laser radiation with the cassette so it can give a real time measurement. The real time measurements give instant information about the underground environment that will allow the mining engineer to take immediate action and enact plans instead of waiting for results from the laboratories where NIOSH 5040 method may take several weeks to get the measurements."

Jan 1, 2016

By J. Fuller, L. Marsden

Windborne dust from alkaline salt flats and mining-related tailings ponds is especially prone to threaten applicable ambient air quality standards. Sodium carbonate crystals, typically present, weather to an exceedingly fine, non-cohesive dust, causing air quality problems for miles downwind. Recently developed specialized polymers react with alkaline dust to form sturdy, wind-resistant crusts with good longevity. An on-going demonstration project at a major trona facility has developed techniques for cost-effective application of these polymers over large areas of soft tailings or sediments in a wide variety of situations. Recently treated areas on the order of 80 acres show effective suppression of dust.

Jan 1, 2004

By Robert V. Price

It is a pleasure to be here today to discuss coal's prospects with the Society of Mining Engineers of AIMS--- a group destined to play a crucial role in shaping our national energy future. Much has been said lately about attaining domestic energy self-sufficiency, but to date, little has been done. Oil tankers from Venezuela and Kuwait continue to glide across the seas to meet our incremental energy needs. Meanwhile, our principal domestic energy resources -- oil and natural gas reserves in the Outer Continental Shelf and the oil shale deposits and the coal lands of the West -remain untapped. Help, however, appears to be on the way. In a forceful address last fall, President Ford called for the elimination of oil as a fuel for base-loaded power plants and its replacement with coal by 1980. He also urged the accelerated leasing of federal lands on the Outer Continental Shelf, the resumption of coal leasing on federal lands, and the development of a new energy conservation policy. There are, of course, many details left to be worked out. Language must be developed to put statutory flesh on the conceptual bones spelled out by the President. Congress must act. Regulations must be approved and tested, if need be, in court.

Jan 1, 1975

By Petr Salak, Adrian St. John, Angelos Gakis

"INTRODUCTIONCrossrail will provide London and the South East of England with a world class, high-capacity railway to ease congestion on London’s public transport system and enable better access between business, residential and entertainment districts. At the heart of this £14.8bn scheme lies Farringdon Station, which will form a major interchange between Crossrail, Thameslink and London Underground. The £400m Farringdon Crossrail station was awarded to a joint venture of BAM Ferrovial Kier (BFK) in 2011, and comprises two ticket halls, two platform tunnels and a multitude of connecting tunnels all constructed using open face sprayed concrete linings (SCL). BFK appointed Dr. Sauer & Partners (DSP) as their specialist SCL designer. As the main contractor for both C300/C410, the Western Running Tunnels and Station Caverns, and also for C435 Farringdon Station, BFK were in a unique position to develop strategies to reduce cost, time and risk for the Client. One such innovation involved the continuation of the TBM drives for the running tunnels right through the length of the new Farringdon platform caverns. This created large diameter precast concrete pilot tunnels for the subsequent platform enlargement using SCL. The benefits of such an approach are described in detail by St.John et al 2015. BFK also introduced another alternative strategy to reduce cost, time and risk, by proposing to abandon the TBMs in the ground (“Turn & Bury”) permanently rather than recovering them through the ticket hall shafts. This de-risked the programme, enabling critical ticket hall construction to proceed unhindered. However, one consequence of this revised strategy was an area of increased underground congestion, with two SCL tunnels (RTE2 and ES2) and a bored tunnel (complete with abandoned TBM) in close proximity to a ticket hall excavation (see Figure 1) and a sensitive, listed railway structure. Faced with this complex geometry, and combined with challenging geotechnical conditions (Gakis et al 2015), the team chose to install enhanced monitoring to study the behavior of tunnel RTE2 and provide additional assurance that the tunnels were performing as predicted. Applying advanced 3D numerical modelling and taking into account the residual tensile strength of the SCL helped avoid unnecessary reinforcement installation in primary lining and/or early installation of a secondary lining in RTE2 prior to ES2 construction."

Jan 1, 2016

By R. L. Sandefur

Any geostatistical study involves (implicit) hypotheses about 1. The distribution function 2. The drift of the data 3. The (underlying) variogram Once these are known, most other results follow from geostatistical theory. However, to date, there have been few theoretical studies on testing these implicit hypotheses. Most of the published studies in this area have dealt with the fluctuation of the variogram or the sampling distribution of the variogram (Journel and Huijbregts, 1978; Davis and Borgman, 1979). Questions regarding these hypotheses regarding a given deposit arise often. Coal geologists often infer channels and washouts on the basis of thicknesses data. Zoning is recognized in a variety of metal deposits. A test as to whether these inferences are valid on just chance occurrences would have widespread application. .It is standard geostatistical practice to "eyeball" fit variograms. In the early exploration phase when just a few pairs are available, the variogram often displays wide fluctuations and there may be considerable doubt about which variogram model to use.

Jan 1, 1982

By P. C. Kapur

The hierarchical relationship between three broad kinds of grinding models for a spatially homogeneous, linear, time-invariant batch grinding system are first established. Limiting and asymptotic arguments for arriving at approximate but simpler models are employed in all three cases. These parsimonious models -provide alternate and, in some respects, more incisive and convenient tools for the analyses of grinding processes and simulation of comminution circuits. In the discrete-size, discrete- time class of models, a reduced mill matrix is derived, which is seemingly adequate for those grinding circuits whose identification otherwise is difficult because of limitations on the quantity of data and its quality. In discrete-size, continuous-time types of models, parameter lumping has been employed for obtaining a G-H solution which is quite accurate and exceptionally useful for graphical display of data, model verification, and parameter estimation and simulation. In continuous-size, continuous-time models, a similarity transformation is used for solving the integrodifferential equation of grinding. This solution provides a unified framework for a number of apparently diverse empirical grinding phenomena such as self-preserving behavior of ground particle size distributions and energy laws.

Jan 1, 1987