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By R. L. Russell

Production at Freeport Indonesia's Ertsberg open pit copper/gold mine started in 1972 at a rate of 7500 t/d. Mill throughput remained at that rate for a number of years until the discovery of the Ertsberg East (GBT) orebody. This discovery prompted three successive expansion stages from 1981 to 1988 that boosted production to 20,000 t/d. The discovery of the huge Grasberg porphyry copper deposit in 1988 launched a new era of much larger expansions. The first of these involved installation of a fourth primary mill in 1989 to bring production up to 32,000 t/d and was immediately followed by an expansion of the crushing and screening plant and the addition of a new south concentrator to bring production to 57,000 t/d in 1991. The addition of a primary ball mill and the changeout of the original Denver flotation cells in 1993 has served to optimize current production at a level of 66,000 t/d. A major expansion is now in progress. This includes construction of another new concentrator to house a SAG mill circuit and large Wemco flotation cells in an area created by the removal of 6,000,000t of glacial material. This current expansion, with a planned completion in 1995, will take production to 115,000 t/d. This paper describes the evolution of the Freeport Indonesia (FI) concentrator to-date and will then go into an in-depth discussion of the 66,000 and 115,000 t/d expansions.

Jan 1, 1994

By Alan Rhodes

This study is initiated to investigate the efficiency of separation of mineral slimes using electroflotation as compared to that of column and conventional flotation techniques. Important parameters such as collector concentration, pH, current density, aeration rate, etc., have been studied. The results indicate that electroflotation can be used more efficiently in processing rutile slimes (10 µ) under certain operating conditions.

Jan 1, 1982

By Brajendra Mishra, Himanshu Tanvar

Niobium and tantalum extraction industries heavily depend on fluoride chemistry for metal oxide production. This study concentrates on developing a fluoride-free approach utilizing alkali treatment for selective dissolution of niobium and tantalum phases. The application of microwave heating in the alkali treatment of columbite significantly reduced the processing time, providing a higher reaction rate and recovery than conventional heating. A short duration of microwave exposure (6 min) elevated the sample temperature to more than 900 °C, resulting in the rapid formation of water-soluble niobium and tantalum complex. Metal recovery from the solution was attempted through direct precipitation using guanidine carbonate as the precipitating agent, resulting in a mixed oxide product with > 90% purity. On the other hand, solvent extraction was also attempted using methyltrioctylammonium chloride as an extractant, providing a niobium oxide and tantalum-rich mixed oxide with > 98% purity as the final product.

Mar 23, 2024

By H. Walqui, J. Drelich, J. Pletka, E. Luhta, E. Raber, J. Wieland, P. Boyd, N. Tervo, D. Herron, S. Boston

Mini-projects studying the flotation chemistry of paper de-inking were incorporated to an educational program at Michigan Technological University with support from the paper recycling industry. Interfacial activity of frothing agents, surfactants and polymers in de-inking flotation systems has been studied through flotation, atomic force microscopy, zeta potential, contact angle, surface tension, and froth stability measurements. These fundamental studies were developed to understand microscopic and molecular effects occurring in flotation of ink particles that may lead to improved designs in de-¬inking flotation processes. Fundamental studies indicate that ethoxylated alcohols are efficient frothing agents in flotation and can be used to clean the recovered paper from hydrophobic ink particles. Next, it was further supported in this research that the fatty acids activated by calcium ions act as collectors in flotation of ink particles. Finally, improvements in de-inking flotation are reported in laboratory tests involving aqueous solutions of polymeric flocculants.

Jan 1, 2001

By Harold L. Lovell

The current interest in sulfur recovery from coal measures is indicated by a recent report prepared for the Public Health Service (1) It was noted that the concentration of pyrites to a product containing 42-48 percent sulfur should be relatively easy with present equipment. It was also pointed out that a utility potential exists for the high-grade iron concentrate which results as a by-product of the consumption of pyrites in the acid-making process. However, economics, marketing characteristics, location, transportation, pyrite levels and coal characteristics all strongly influence the feasibility of fostering industrial development of such processes. The extent of pyrite recovery and product quality is intimately related to pyrite particle size and its degree of liberation, a consideration usually given greater emphasis in metal ore preparation than in processing coals. Consequently, fine crushing to nearly 20 mesh probably will be essential for maximum practical processing. It appears that any process separating pyrites from a coal must involve a reprocessing of the normal preparation plant refuse, although some yields can be attained from certain existing operations as products from, a shaking table or a jig. Further, the existence of millions of tons of coal refuse cannot be ignored as a mined source of raw materials. The recovery of saleable products from such wastes, although untried on a large scale under current conditions, not only offers a realistic source of sulfur but also would achieve a secondary refuse with the minimal contents of substances which incite and propagate the burning of organic and inorganic combustibles. These silicate materials, thus beneficiated, also offer some potential for economic utilization. Some significant tonnages of pyrites have been produced from coal measures in the past, but the experience was, in general, not consistent with current coal preparation practice. The processes involved did not include cyclones and heavy media; nor were they carries out under the sociological environment concerned with pollution as exists today.

Jan 1, 1967

By C. Vass, A. Noble

"The chemical treatment of mine-influenced waters is a longstanding environmental challenge for many coal operators, particularly in Central Appalachia. Mining conditions in this region present several unique obstacles to meeting NPDES effluent limits. Outlets are often located in remote areas with challenging terrain where conditions do not facilitate the implementation of large-scale commercial treatment systems. Furthermore, maintenance of these systems is often laborious, expensive, and time consuming. Many large mining complexes discharge water from numerous outlets, while using environmental technicians to assess the water quality and treatment regime multiple times per day. As an alternative solution, this paper describes the ongoing research and development of automated chemical treatment systems for mine water discharges. The current work explains the development of a bench-scale prototype that has been used to evaluate various monitoring, notification, and control strategies. Results from this testing are compared to present day practices to show the costs and benefits of implementing an automated treatment and monitoring program. INTRODUCTION Background The National Pollution Discharge Elimination System (NPDES), per Section 402 of the Clean Water Act, requires permitting of all point source discharges from coal mines. This program dictates that all water leaving a permitted boundary, whether it be process water or storm water, must leave through a monitored NPDES outlet. These permitted NPDES discharge points, also denoted outlets, outfalls or monitoring points, must meet a rigorous set of effluent limits to maintain compliance. Common effluent limits monitored by coal companies include but are not limited to iron, manganese, aluminum, total suspended solids (TSS), and pH. Raw mine water is often deficient in meeting these effluent limits, and as a result, various treatment processes are required to bring the water into compliance prior to environmental release. Depending on the mining and geologic conditions, water monitoring and treatment programs can constitute a significant operating cost for the mine operator. In Appalachia, acid mine drainage (AMD) constitutes one of the most significant and widespread water quality challenges that must be treated per NPDES guidelines. AMD is a general lowering of water pH that occurs when water and sulfide minerals interact within oxidizing conditions in coal and metal mining. Acid Rock Drainage (ARD) is a similar term that applies more generally to non-mining causes such as highway construction and other large-scale excavations. Today, mine influenced waters (MIW) is becoming more popular as the general term referring to all types of mining-induced water issues. AMD has been researched substantially over the last 30 years, with investigators studying various causal mechanisms and treatment strategies (e.g. Gazea, 1996; Ziemkiewicz, 1998; Skousen, 2000; Kleinmann, 2001; Johnson, 2003; Akcil, 2006; Kalin, 2006). This research has produced several pragmatic results, which provide numerous methods to predict, prevent, and treat AMD."

Jan 1, 2016

Refractory gold concentrates often contain submicroscopic gold that is encapsulated within the crystal matrix of iron sulfide minerals, such as pyrite, pyrrhotite and arsenopyrite. To recover the gold, the host mineral must generally be broken down chemically by oxidative processes, such as roasting, pressure oxidation or bacterial leaching, which expose the gold for subsequent recovery by leaching in cyanide solution. The focus of attention in these pretreatment processes is usually the oxidation of the sulfides to elemental sulfur, sulfur dioxide gas or sulfate ions. Less attention is paid to the deportment of iron and the changes in its oxidation state, although this can have a profound effect on gold and silver liberation, as well as downstream operating costs. Iron sulfide minerals break down completely during pressure oxidation, and dissolve in the sulfuric acid solution that is gener-ated from oxidation of the sulfides. This dissolution liberates the tiny gold particles that were originally trapped in the sulfide crystals, and gold recovery during subsequent cyanidation is usually very high (>95%). Iron goes into solution in the oxidation process, initially as ferrous sulfate, but this compound is rapidly oxidized to ferric sulfate, which then hydrolyzes and reprecipitates. The form of the precipitate varies depending on the operating conditions in the autoclave and the presence of certain metal cations. When the acidity in the autoclave is quite low (<20 g/L H2SO4) and the temperature is high (>200°C), the formation of hematite is favored. When the acidity is high (>20 g/L H2SO4) and the temperature is relatively low (160 to 200°C), the formation of basic iron sulfate is favored. If the ore or the leach solution contains significant levels of certain cations (such as Na+, K+, NH4+, Ag+ or Pb2+) and the acidity is high (>20 g/L H2SO4), jarosite compounds are favored. Hematite is the desired iron product in the autoclave discharge, for both metallurgical and environmental reasons, but it is difficult to operate an autoclave under the conditions required for effective liberation of gold without converting some of the iron to basic iron sulfate and/or jarosite. These compounds fall into a category of iron compounds known generically as iron hydroxy sulfates, all of which can cause significant processing and environmental problems in the downstream gold process. This paper deals specifically with basic iron sulfate: the conditions under which it is formed in an autoclave, the problems that are caused by its presence in the feed to a cyanidation plant and possible remedial strategies that can be adopted, both in the autoclave and downstream.

Jan 1, 2010

Refractory gold concentrates often contain sub-microscopic gold that is encapsulated within the crystal matrix of iron sulphide minerals such as pyrite, pyrrhotite and arsenopyrite. To recover the gold, the host mineral must generally be broken down chemically, by oxidative processes such as roasting, pressure oxidation or bacterial leaching, which expose the gold for subsequent recovery by leaching in cyanide solution. The focus of attention in these pre-treatment processes is usually the oxidation of the sulphides to elemental sulphur, sulphur dioxide gas or sulphate ions. Less attention is paid to the deportment of iron and the changes in its oxidation state, although this can have a profound effect on gold and silver liberation, as well as down stream operating costs. Iron sulphide minerals break down completely during pressure oxidation, and dissolve in the sulphuric acid solution that is generated from oxidation of the sulphides. This liberates the tiny gold particles that were originally trapped in the sulphide crystals, and gold recovery during subsequent cyanidation is usually very high (>95%). Iron goes into solution in the oxidation process, initially as ferrous sulphate, but this is rapidly oxidized to ferric sulphate, which then hydrolyzes and re-precipitates. The form of the precipitate varies depending on the operating conditions in the autoclave and the presence of certain metal cations. When the acidity in the autoclave is quite low (<20 g/L H2SO4) and the temperature is high (>200OC) the formation of hematite is favoured. When the acidity is high (>20 g/L H2SO4) and the temperature is relatively low (160 to 200OC), the formation of basic iron sulphate is favoured. If the ore or the leach solution contain significant levels of certain cations (such as Na+, K+, NH4+, Ag+ or Pb2+) and the acidity is high (>20 g/L H2SO4), jarosite compounds are favoured. Hematite is the desired iron product in the autoclave discharge, for both metallurgical and environmental reasons, but it is difficult to operate an autoclave under the conditions required for effective liberation of gold without converting some of the iron to basic iron sulphate and/or jarosite. These compounds fall into a category of iron compounds known generically as iron hydroxy sulphates, all of which can cause significant processing and environmental problems in the downstream gold process. This paper deals specifically with basic iron sulphate; the conditions under which it is formed in an autoclave, the problems that are caused by its presence in the feed to a cyanidation plant, and possible remedial strategies that can be adopted, both in the autoclave and downstream.

Jan 1, 2010

By L. B. Hales

December 3, 1972, James Wm. White presented the results of an instrumentation and process control survey which was sponsored by the Anaconda Company at the annual Tucson Subsection AIME meeting.(1) Twenty-six responses were obtained from questionnaires sent to 48 operating plants throughout the world. The survey results were discouraging in that there were more failures and problems than examples of success. The following quotes are taken from the text of the paper. "We run our mill by the seat of our pants." &apos;If these blue sky Ph.D.&apos;s (in the instruments and controls area within research) had some operating experience they wouldn&apos;t make a lot of the suggestions they do."

Jan 1, 1981

By C. Alexander

Stillwater Mining Company is developing a second underground palladium and platinum mine approximately 21 km (13 miles) west of their existing Nye operation in south central Montana. A 5650 meter (18,550-foot) tunnel is required to gain access to the ore bearing horizon (J-M Reef). Access and primary mine development can be accelerated through the use of two 4.6 meter (15-foot) diameter tunnel boring machines (TBM). One TBM was purchased new while the other was purchased used. Machine specifications, site support facilities, portal/launch chamber construction, TBM assembly, startup and operation are discussed in this paper.

Jan 1, 1999

By Robert L. Marovelli

The major mining health and safety problems of concern to United States Government and private industry researchers in 1981 included the difficulty experienced by longwall operators in complying with the Federal 2 .0-mg/m3 respirable dust standard, the accident rate associated with falls of ground and materials handling hazards, and the upsurge in the incidence of disasters after the steady decline in recent years. Although the many mines and manufacturing companies involved in the research projects to be described are not specifically identified, it is important to note their significant involvement. This is not by way of acknowledgement, but rather to establish that these projects, using mostly Federal funds, represent close cooperation between the U.S. Government and the mining industry. The ongoing work to be described on the development of critical longwall dust control technology is a classic example of Government-industry participation through the phases of problem identification, planning, cost-sharing, and implement at ion.

Jan 1, 1982

By James M. Barker

Industrial minerals are critical to most aspects of modern society. They are pervasive in both industry and in everyone&apos;s lives (McVey, 1989; Barsotti, 1993). They are also the dominant class of minerals produced in the United States but this fact is little known outside the industry. For example, in 1993 (U.S. Bureau of Mines, 1995, table 1) industrial mineral dollar value was double that of metals ($20.86 billion vs. $10.88 billion) and employment levels were nearly so (74,000 vs. 40,000). A further difference is that transportation tends to dominate production costs (FOB end user) whereas they are much less significant in other mining ventures or other industries. Finally, metal mines are more concentrated west of the Mississippi; industrial mineral operations are more prevalent to the east (U.S. Bureau of Mines, 1995, p. 16-17). The significance of transport cost is discussed in Part 2, which is essentially Barker and Austin, 1995. Part 1 will update and expand portions of Barker and Austin (1995) and provide a more detailed discussion of import/export relationships using a China/United States reference point because of China&apos;s dramatic influence on some industrial mineral markets since the mid-1980s (barite, etc.).

Jan 1, 1996

By Jamal Rostami, Alireza Salimi, Christian Moormann

"Rock mass classification systems are often applied in many empirical design practices in rock engineering, some contrasting with the original intent and applications of these classification systems, for example, estimation of TBM performance in various ground conditions. While accurate estimation of machine performance is significantly impacted by rock mass properties, parameters used in many of the existing classifications are more related to ground support design and not rock mass boreablity. The results of many investigations on this issue have shown a weak correlation between TBM rate of penetration and rock mass classification. This limitation can be overcome by fine tuning the rock mass classification input parameters to represent influence of rock mass properties on TBM performance as has been the objective of RME or QTBM. This paper will offer an overview of the impact of rock mass on TBM performance and introduces an empirical equation for predicting performance of rock TBMs based on rock mass classification. The results of the preliminary analysis of a new model has revealed that the use of the proposed system can offer a reasonable accuracy for estimation of TBM performance in various rock masses. 1. INTRODUCTION Hard rock tunnel boring has become more or less the standard method of tunneling for tunnels of various sizes with lengths over 1.5–2 km. Estimating the performance of TBM is a vital phase in tunnel design, and for the choice of the most appropriate excavation machine. During the past three decades, numerous TBM performance prediction models for evaluation of TBM rate of penetration and advance been proposed. In brief, all the TBM performance prediction models can be divided into two distinguished approaches, namely theoretical and empirical ones (Rostami et al., 1996). The most common and recent works on this topic are summarized in Table 1. Currently, two models including Colorado School of Mines or CSM (Rostami and Ozdemir, 1993; Rostami, 1997) and Norwegian University of Science and Technology or NTNU (Blindheim, 1979; Bruland, 1998) models are the most recognized TBM performance prediction and prognosis models in use around the world."

Jan 1, 2016

By M. G. Hester

The ore reserve modeling of stratiform uranium deposits to be mined by selective underground mining methods must be done with consideration of the erratic nature of the ore forming processes that produced the mineralization. Estimation methods that model the uranium grade as a smooth transition between high grade and low grade drillhole intercepts tend to greatly overestimate the ore tonnage. Care must be taken to first establish realistic ore pod geometries and then estimate the grade of the reserve units within the pods.

Jan 1, 1985

By F. L. Jackson

The large scale transportation and storage of sulphur in the liquid state is a relatively new development, but is really only a logical extension of old mining and processing techniques, It is not known who the first person was to win a relatively pure sulphur from ore by melting, but this method was commercially used at least two hundred years ago in Sicily and is still in use today. The Frasch process of mining was invented over sixty years ago, and the development and improvement of-liquid sulphur pumping and handling techniques has paralleled the growth in the Frasch mining industry. During the last fifty years, improvements in the technology of using sulphur have included the premelting of sulphur prior to its being burned for acid production or conversion into CS2 and other compounds. Yet, until fairly recent times, sulphur produced as liquid has been solidified into large blocks at the producing point, broken down by blasting or with mechanical equipment, and shipped in bulk form as a solid.

Jan 1, 1962

By S. G. Dixit

Alunite (KAl3(SO4)2(OH)6] is one of the important nonbauxitic resources for aluminum in U.S.A. The major gangue material associated with a unite ore body is quartz. Experimental results indicate that oleic acid flotation of alunite is quite effective in upgrading the ore. The flotation chemistry of the alunite/oleate system has been investigated using various techniques such as: hallimond tube flotation response, measurement of adsorption density using I4C labeled oleated, electrokinetic measurements, infrared spectral studies, contact angle measurements and thermochemical measurements using an isothermal microcalorimeter. Alunite has been found to float readily with oleate in the pH range 4-10.5 and its flotation response is enhanced at higher temperatures. The PZC of alunite has been determined to be at pH 7.2 ± 0.15 which agrees with what would be predicted from solution chemistry and from the flotation response with physically adsorbed collectors. Infrared spectra show a specific peak in the range 1585-1600 cm-1 which has been attributed to the formation of an aluminum oleate surface species. Both adsorption density measurements and infrared spectra indicate that during adsorption multilayers are formed. The heat of adsorption of oleate on alunite has been found to be endothermic and of the order of 4-6 KJ/ mole.

Jan 1, 1980

By D. Blackwell, W. R. Reed, G. Ross, S. Peters, M. Shahan

Dust collectors for roof bolting machines generally use a dry box to collect the roof bolting material. Recently, an underground mining operation converted a dry box dust collector to a wet box dust collector with a unique exception from MSHA for testing purposes. Water is routed to the roof bolter from the main water line of the continuous miner. The wet box utilizes a water spray to wet the incoming material. Testing was conducted comparing the two different collector types. Respirable dust concentrations surrounding the roof bolter with the different collection boxes were similar. The main difference in respirable dust concentrations occurred when cleaning the dust boxes. The average respirable dust concentration during cleaning of the wet box was 0.475 mg/m3, and during the cleaning of the dry box the average respirable dust concentration was 1.188 mg/m3. The silica content of the roof material was high, ranging from 28.9% to 52.7% during this study. The results from this study indicate that using the wet box as a collector reduced exposure to respirable dust up to 60%when cleaning the collector boxes. INTRODUCTION Currently, the dry vacuum dust collection system is the standard dust collector on roof bolters in underground coal mining. It has been proven to be an effective dust control to prevent roof bolter operators’ overexposure to coal mine respirable silica dust during roof bolting operations [Potts eta l, 2011 and Colinet, 2013]. The dry collection system works as follows: drill cuttings are vacuumed into the precleaner. The precleaner dumps oversized material onto the mine floor while undersized material enters the dust box via vacuum airflow produced by a blower. The cuttings entering the dust box are either deposited on the floor of the dust box or into a dust collector bag. The vacuum airflow leaves the dust box through a final filter which removes any small particles from the airflow. Figure 1 shows the internal view of two dry collection system boxes; one that does not use the dust collector bags and another that uses the dust collector bags. Dust collectors that use dust collector bags to contain material inside the dust collector box have been shown to provide better protection to roof bolter operators than dust collectors that do not use the bags [Listak and Beck 2008]. The dry collectors are very efficient at reducing respirable coal mine dust exposure from roof bolting activities. Recently, Blue Mountain Energy’s Deserado underground coal mining operation, outside Rangely, CO, made a modification to the dry collector system to convert it to a wet collector system with a unique exception from the Mine Safety and Health Administration (MSHA) for testing purposes. The wet collector system still uses a vacuum system to pull material from the vertical roof bolt hole, but incorporates a water spray nozzle located inside the dust box to wet the incoming material. The flow through the nozzle ranges from 1.9–7.6 lpm (0.5–2.0 gpm) at 0.69 MPa (100 psi). The conversion to the wet collector system removes the precleaner and the cyclones inside the dust box. The wet material (sludge) then empties through a specialized valve in the bottom of the box. The final filter is still used to prevent respirable dust from leaving the dust box through the exhaust. During operation, the wet collector dust box is opened and hosed clean after roof bolting every place. After every two entries the final filter is changed out. Figure 2 shows the inside of the wet collector box.

Jan 1, 2019

By William H. Dresher

A recent report to President Reagan from the Business-Higher Education Forum, entitled, "America&apos;s Competitive Challenge: Need for a National Response," (1) observes that in the recent past, ". . . much of that research, which is necessary for major breakthroughs and sustained productivity improvements, was redirected to short-term objectives ... At the same time, American universities, which conduct more than half of the nation&apos;s basic research, have suffered from an accumulated under-investment in facilities and equipment amounting to an estimated $1-4 billion." Also contributing to the decline in America&apos;s productivity, the report said, are "...weak technology transfers between government and industry and between universities and industry..." This report as well as other recent reports and articles have, reopened a subject which has long been debated but rarely resolved-- the interaction between the academic community and industry in the sponsorship and conduct of research. The subject is unfortunately, too often treated as a controversial issue involving ethics and the profit motive when, in fact, the two branches of society -- industry and academia -- are necessarily part of the same system. I would like to speak to you today on the subject of university-industry interactions and to some extent discuss the role of government in such interactions. Finally, I will make some remarks as to how this subject applies to the mining industry.

Jan 1, 1984

By Ernest N. Wolff

You here are all familar with the myriad of new laws, some enacted and some pending, that affect the mining industry. These laws, for example those dealing with suspended matter, affect us in Alaska as they do you. Likewise, our friends in government, the Geological Survey and the Bureau of Mines, provide us with the same fine services that they do elsewhere. I am not going to speak today about these, but concentrate on one act of Washington, D.C. the impact of which is felt, for now at least, principally in Alaska. A little more than a year ago, I spoke in Spokane on the subject, "Governmental Challenge to Mineral Development in Alaska." I outlined some of the policies of Government which were operating to change the rules under which the industry operates and to alter the relation- ship between government, industry, and the individual. At that time the Native Claims Settlement Act had not been passed, but was on the verge of being so. In reading over what I said in Spokane, I note that I touched on many points where Government was actually challenging mineral development in Alaska. With the passage of the Alaska Native Claims Settlement Act, many of these actions were given a cloak of legality, and machinery was set up to concentrate the drive to tie up the public domain, machinery which will allow govern- mental control and interference with the actions of individuals on something like 90% of Alaska&apos;s land surface. This remarkable law is going to affect each and every one of you. Now, a year after its passage, we are only just beginning to see its lesson for the future. It was created by a coalition of powerful groups, who got other groups to support them by promising to deliver something they had no intention of delivering. Alaskan issues are again being used to get various groups not to oppose legislation which will severely harm them. It will help to understand the nature of this new drive if we understand the Native Claims Act and how it came into being.

Jan 1, 1973

By Dai Wang

Stoppings are necessary ventilation control devices for effective air distribution underground. However, one of the major problems underground mining has is that every stopping is a potential leaking source. Since air always flows from a point of high pressure to one of lower pressure, and the total pressure at every point in intake airways is higher than that in the return airways, air will always tend to leak from intake to return (Tien, 1996). In many mines, less than half of the air entering the mine actually gets to the working areas; the rest of it simply short-circuits directly to return airways through leaky stoppings instead (Timko and Thimons, 1983). Leakage through a stopping occurs because of pressure drops across the stopping and available leaky path in stoppings. Empirical equation has been widely used to characterize the relation the amount of leakage and variables that affect leakage. However the use of this equation requires accurate information for constants which are not always readily available. It is the attempt of this paper to derive an equation similar to the Atkinson Equation that can readily be applied to characterize pressure-leakage relationship for any given stopping.

Jan 1, 1998