Search Documents

By John W. Buch

Safety and cost in mining coal beds under the extreme pressures found at depth, full extraction to conserve resources, and even surface subsidence to minimize damage of improved areas have directed much well-deserved attention, in the United Kingdom; to roof-control methods. Because the effects of pressure will be felt intensely as our Pennsylvania anthracite mines grow deeper, the senior author took advantage of an opportunity afforded by a mission to Europe3/ to observe, to a limited extent, the effects of pressures found in deep mines and the manner in which they are con trolled. Organized research relating to strata control has been carried on in Great Britain for nearly 25 years. These activities have been ably outlined by Dr. D. W. Phillips.4/ Physical properties of coal-measure rocks, movements of roof and floor, and types of face and roadway supports have been investigated. Same of the forces induced by the extraction of coal have been measured. The results of this research have been publicized and openly discussed, and much progress has been made in establishing a better factual understanding of roof-control problems and their solution.

Jan 1, 1951

By W. -S. Hwang, R. A. Stoehr, P. Ingerslev

"The flow of molten metal entering complex two-dimensional foundry molds has been modeled using the Simplified Marker and Cell (SMAC) and Solution Algorithm (SOLA) techniques. The molds were for a series of four and three-spoke wheel designs. The computer calculations were compared to physical experiments in which molten cast iron was poured into C02-bonded sand molds. The metal was photographed with a high speed motion picture camera focused through a Pyrex glass window on one face of the mold. To get good agreement between the calculations and the experiments, it was necessary to accurately represent the velocity through the ingate. This was calculated by application of the Bernoulli equation to flow through the feed system. Some difficulties were experienced with mathematical instability, expecially in the three-spoke design with a narrow ingate. This was overcome by using 100% upwind differencing, and over relaxation parameter near 1.0 (i.e. no over relaxation), and variable mesh spacing.IntroductionModeling the flow of molten metal entering molds has the potential for making significant contributions to the design of feed systems. It will supply information to the computer-aided-design systems of the future that will enable the designer to optimize the placement of gates, dimensioning of passages, and designation of casting speeds. Such design criteria have generally been based on application of energy balance (Bernoulli equation) principles to flow in the sprues, runners, and gates. Indeed, this is the easiest way to determine the proper dimensions to give a suitable filling time for a casting of a given size. A number of computer programs, including one by some of the present authors, have integrated such calculations into CAD systems. l Modeling the flow of metal inside the mold cavity requires other techniques that will handle free-surface transient flow. Stoehr and Hwang reported on the application of the Marker-and-Cell (MAC) technique to mold filling problems at the previous conference in this series at Hennicker, N.H. in 1983. 2 Although considerable progress has been made since that time in improving the accuracy, stability, and convenience of these techniques, the shapes to which they were applied remained limited. Also, physical verification of the results of the calculations was limited to water models.The work to be reported in this paper was undertaken with two objectives: (1) to apply these techniques to more complex and realistic shapes, and (2) to verify the results by comparison with flow patterns observed in molten metal poured into actual sand molds."

Jan 1, 1986

By Albert L. Toenges

The State Division of Geology Arkansas Resources and Development Commission, and the Arkansas-Oklahoma Coal, Operators Association requested assistance from the Bureau of Mines in a study of coal-mining methods and practices in .Arkansas coal mines with the objective of reducing production costs. On October 7, 1946, a joint meeting was held by representatives of the Arkansas Resources and Development Commission, approximately 30 coal-mine Operators of the Arkansas -Oklahoma Coal Operaters Association, and representatives of the Bureau of Mines. The many problems confronting the coal industry in Arkansas, including mechanical mining in thin beds, costs, labor, and working time were discussed. Following this Meeting, a joint letter from Harold B. Foxhall, State geologist, and -P. R. Stewart, commissioner, Arkansas-Oklahoma Coal Operators Association, was addressed to Dr. R. R. Sayers; former ,Director of the Bureau of Mines, requesting that mining conditions in Arkansas be studied.

Jan 1, 1949

By B. Arvidson

Computer-controlled machine sorting may, if properly applied, have a dramatic effect on overall economics of a mine operation. Radiometric and photometric sorters have been used for many years and new developments will be reported, such as a sorter for fine particles and a conductivity/magnetic sorter. Application examples with emphasis on precious metals will be given. Economics for some of the projects will be reviewed and discussed. Sorting underground is shown to be particularly attractive, but machine sorting would be profitable in most cases based on savings in transportation and milling/beneficiation costs only.

Jan 1, 1987

By S. Kelebek, U. Demir, T. C. H. Richards, E. Koss

"Laboratory-scale tests were carried out to investigate the response of a high-grade (~143 g/tonne) well-liberated gold ore to flotation using two collector types. Octyl and amyl xanthates, representing conventional types of collectors, were tested against an n-octanoic and hexanoic acids under moderate and high redox potential conditions. The latter was based upon a suggestion in literature that monocarboxylic acids are able to adsorb onto the surface of gold at redox potentials near 600 mV (SCE). This investigation did not demonstrate that these carboxylic acids could function as collectors for gold in real ores. In fact, they appear to have slightly depressed gold. However, the results demonstrated that octyl and amyl xanthates acted as highly effective gold collectors for this ore and that an increase in the collector dosage led to an increase in recovery for all mean particle sizes. In some tests, gold recoveries of around 95% were attainable in concentrates with grades around 6 kg/tonne, indicating that xanthate flotation remains a viable means of concentrating gold even at coarse grain sizes. Various aspects of the process such as grade-recovery performance and recovery by size are discussed.INTRODUCTION Three methods are used for the recovery of gold in mineral processing, either alone or in combination: gravity concentration, cyanidation and flotation. Gold occurs as a by-product in some ores together with platinum group metals and as the primary metal in other ores in the form of native gold and electrum, which are alloys of gold, silver and minor amounts of copper. Flotation is a viable method for recovering liberated gold where the gold is visible under an optical microscope (greater than 1 µm in size) and where the attachment of gold grains is not prevented due to bubble loading by competing minerals. It is generally known that grains finer than 150 µm in size will float with most collectors."

Jan 1, 2017

By A Mortazavi, M Akhmedya

Mining is recognised as being one of the most dangerous industries in the world due to the difficult working conditions. Working in such hazardous circumstances in an underground mine often results in a variety of accidents. The working conditions at Kazakhstan’s underground mines have deteriorated owing to a lack of a risk-reduction plan and methodology. This paper evaluates different underground mines in Kazakhstan and demonstrates the employed mining method and the observed failure modes. Risk assessment has long been recognised as a valuable technique for preventing accidents. In the underground mining sector, risk assessment tools play an important role in avoiding work-related accidents. However, geotechnical uncertainty is a significant source of severe incidents like stress-induced roof collapse, wedge failure, seismicity etc, which result in human and financial losses. A geotechnical risk assessment performed early in the mine design process might assist justify a different mine design component, such as different support systems for a dangerous location within the mine openings during mining. The goal of this research is to create a damage/failure database aiming at the development of a geomechanical risk assessment methodology. This work identifies a thematic structure linked to risk assessment and management for the examined Kazakhstan mining sector. As part of the developed database, the dominant modes of failure within the Kazakhstan underground mining conditions were investigated. The study will provide opportunities to establish future research objectives for Kazakhstan’s mining industry where there are significant gaps between state-of-the-art research and mining operations in practice.

Nov 29, 2022

By C. O. Stee

Introduction The property of Siscoe Gold Mines, Limited, is located on an island of three hundred and forty acres in lake Kienawisik, about fifty-two miles east of Noranda and forty-three miles south of Amos, Quebec. Lake Kienawisik is a part of the Harricanaw drainage system and is crossed by the main line of the Canadian National railway at Amos. This waterway is navigable for boats with a draught of six to eight feet. Diesel engines have been the source of power at the property since milling operations were commenced in January, 1929. The power plant as first designed and built was for a milling capacity of 100 tons. Two Polar-Atlas units, each of 200 h. p., comprised the original installation. With the growth of the 'mine, more engines were added until, at the present time, there is installed at the Siscoe what is rated the largest Diesel plant at any mining property in Canada. Definition of a Diesel 'The Diesel engine is an internal combustion engine which works with liquid fuel introduced after, and independently of, the air charge at a time when communication between the cylinder and the outside atmosphere is cut off, and which ignites the fuel by compression-beat and stored combustion-heat unassisted by heat sources outside the cylinder itself while the engine is in stable operating condition"(1).

Jan 1, 1934

"The paper treats the spatial aspect of mine sequence optimization. This aspect is revealed in the context of determination of the optimum number of cutbacks of an open pit mine. Cutback mining is a dominating method currently in base\precious metal mining and it is based on a pseudo-economic discretization of the pit space by using advanced pit design algorithms. The result of the implementation of such approach of pit design is the generation of pit shells, which need to be grouped into an optimum number of cutbacks for maximization of the project value. A mathematical solution of this problem is developed with the utilization of a combinatorial analysis. The solution provides a multi-variant investigation of the optimum mine sequence with the implementation of an author’s method for production scheduling optimization, which uses the Net Present Value as a criterion for assessing the economic efficiency of mine sequencing. A case study is provided for the conditions of a hypothetical open pit gold mine to illustrate the applicability of the approach. The results obtained reveal the complex nature of the variation of the Net Present Value as a function of the cutback geometry. INTRODUCTION The mine sequence optimization in open pit mining is a procedure that predetermines the efficiency of the production scheduling optimization. From a technological standpoint, the mine sequence optimization deals with two aspects – spatial and time. Each of them plays a tremendously important role in searching for the optimum solution of the open pit design problem. Original results on the time aspect of mine sequence optimization are published by Halatchev [2002]. They reveal a wide range of the Net Present Value (NPV) variation for a multi-variant arrangement of mine sequence over time and using a fixed geometry of the cutbacks, which determines the economic potential of a single open pit mine from a deterministic standpoint. The results show a range of NPV variation up to 30% depending on the stripping ratio of the mine. The effect of this variation is mainly due to the implementation of the mine planning principle of waste deferment in the scheduling optimization and using all theoretically possible variants of mine sequence arrangement by the inclusion of the bench sequences over the Life-Of-Mine (LOM) in the production process."

Jan 1, 2015

By J. C. Barrett

Bureau of Mines research on the arc welding characteristics of titanium was initiated in 1948. Little was known about the art except that the easily contaminated metal required more protection from the atmosphere during welding than most other metals. Chambers were designed and built within which titanium could be welded with adequate inert gas protection. Welds were made and their properties studied, and prototype items were made successfully. This report, presenting a resume of the titanium arc-welding experiments undertaken by the Bureau of Mines, demonstrates that the process is successful if conducted under proper conditions and describes the welding of prototypes. INTRODUCTION The Bureau of Mines' first report on methods of joining titanium covered the subject of spot welding,4/ outlining the conditions necessary for producing spot welds in ductile titanium consolidated by powder metallurgy methods and describing the characteristics of such welds. This report embraces the field of fusion weld-ing of titanium and traces the development of suitable methods and equipment for producing such welds.

Jan 1, 1956

By Jr. Watts, B. K. Cantrell, D. H. Carlson, K. L. Rubow, S. T. Bagley

"Permissible exposure limits (PELs) have been established for gaseous pollutants, carbon monoxide (CO), carbon dioxide (CO), nitric oxide (NO), nitrogen dioxide (NO2), and some gas-phase hydrocarbons emitted in diesel exhaust. There is, as yet, no PEL recommended for diesel exhaust aerosol (DEA), nor is there a standard method for sampling this aerosol.The University of Minnesota and the U.S. Bureau of Mines have collaborated to develop a personal diesel exhaust aerosol sampler (PDEAS) which utilizes size-selective inertial impaction and gravimetric analysis. During the field tests of this sampler, numerous air quality measurements were made in underground coal mines that use diesel equipment.The mine mean DEA concentrations for the five mines surveyed, determined with the PDEAS in the haulageway, was 0.89 mg/m3, with a standard deviation of 0.44 mg/m3. DEA contributed 52 % of the respirable aerosol at this location.In three of the mines filter samples were collected for DEA-associated polynuclear aromatic hydrocarbons (PAHs) and biological activity determinations. Two of the mines were also monitored for the major gaseous constituents found in diesel exhaust. In general, the PAH and biological activity levels were similar for all three mines, and indicate that up to 25 % of the haulageway concentrations may be contributed by outby diesel vehicles. Measured concentrations of CO, CO2. NO, NO2, and SO2, were well below regulated levels.INTRODUCTIONDiesel exhaust contains pollutant gases, such as carbon monoxide, carbon dioxide, nitric oxide, nitrogen dioxide, and gas-phase hydrocarbons, as well as DEA. Much of the health-related concern focuses on DEA and associated organic compounds (Watts, 1992a). A wide variety of these PAHs have been identified and some are known carcinogens and/or mutagens. The U.S. Mine Safety and Health Administration (MSHA) has proposed new PELs for these and other contaminants (MSHA, 1989). MSHA has also published an advance notice of proposed rulemaking to establish a separate PEL for diesel particulate (MSHA, 1992)."

Nov 1, 1995

By Haragobinda Srichandan

The present study aimed to investigate the bioleaching efficiency of moderate thermophilic microorganism in a growth medium without Fe supplement on three different size fractions of spent catalyst obtained from petroleum refinery. All the experiments were conducted on shake flasks at a temperature of 65 °C and a pulp density of 10% (w/v) on three size fractions viz. 45-106 µm, 106-212 µm and >212 µm and a working volume of 100 ml comprising of 10 ml of microbial inoculums and 90 ml of Modified Kelly medium. The parameters like pH, redox potential, viable planktonic cell count and the amount of acid addition was measured and quantified on regular basis to follow the progress of the bioleaching. The pH varied much in the lag and logarithmic phase of the experiments but stabilized toward the stationary phase. The total acid additions in each batch experiment were determined the amount of Conc. H2SO4 requirement, which ranged between 683-757 kg/ton of spent catalyst. The redox potential values ranged between 625-650 mV, Ag/AgCl, but were very low ranging between 350-450 mV during initial period. The planktonic viable cell count ranged between 108-109 cells/ml active in the bioleaching system, without any toxic influence of the spent catalyst, but initially due to fall in redox potential and new environment for the microbes, their population was low. The leaching yield of Ni was found to be promising with very high leaching yield of 92-96% followed by Al as 61-62%, which means both Ni and Al leaching were favored by the moderate thermophilic bioleaching compared to the mesophilic bioleaching. There was very little difference in the leaching yield, when compared with different size fractions and hence grinding can be avoided prior to leaching. This process seems to be economical as no Fe source is supplemented together with no requirement of grinding and over all a biological process resulting for an eco-friendly process for future optimization of the metal recovery from petroleum refinery spent catalysts. Keywords: bioleaching, spent catalyst, thermophile, 9K medium

Sep 1, 2012

By P. D. I. Honeyman

DURING 1938 many copper companies again felt the economic pinch and smelter operations were often on a reduced basis which some- times resulted in intermittent operations and complete shutdowns. During the last half of the year production was stepped up and smelting operations resumed a more normal appearance. One of the present-day trends in reverberatory sme1ting is definitely toward high-tonnage operations. i\ t the Phelps Dodge Corporation's Douglas plant, the reconstructed 107 by 26- ft. reverberatory furnaces are operated at the rate of 1000 tons of solid charge per day. The arch, all of silica brick; is sufficiently high above the bath to give

Jan 1, 1939

By H. Marquis

The present paper consists of a survey of the literature on the problems of abrasion and wear of metals and materials by suspended matter. This problem is a very general one in industry, and is especially notice-able in the operation of cyclones and other types of dust collectors. The problem of abrasive dust in corrosive gas environments, such as commonly encountered in metallurgical industries, is particularly severe. Very little work has been done in the study of this type of abrasive wear, especially at high temperatures. However, a general review is presented here of all the work published on related subjects, such as that involving sand erosion in turbines and water wheels and the effect of temperature on friction wear. Topics in this paper include: blasting wear by sand, quartz, limestone, silicon carbide and other refractory particles; methods of investigation; effects of velocity, temperature and *Canadian Armament Research and Development Establishment, Valcarter, P.Q. angle of attack; correlation between indentation hardness, scratch hard-ness and resistance to abrasion; the effect of protective coatings; resistance of various metals; etc.

Jan 1, 1962

By C. R. Van Hise

PART I.-GENERAL PRINCIPLES. [ ]

Jan 1, 1902

By Zoheir Khademian, Gabriel S. Esterhuizen, Morgan Sears

Based on the 2010-2019 Mine Safety and Health Administration (MSHA) accident report database, 91% of reported ground control accident in the US longwall mines were caused by gateroad roof instability. This can be related to the significant changes in loading conditions that gateroads are subject to from the development to the longwall abutment loading phases, combined with the thinly bedded shale roof, found in many US longwall coal mines. One of the challenges in designing efficient support systems is to understand the roof instability mechanisms along with support-roof interactions under this complex loading condition. Field monitoring of roof displacement and stress changes coupled with detailed analyses using numerical models are well-documented techniques to study the causes of roof instabilities. However, traditional modeling techniques require additional calibration to simulate delamination and buckling of shale roof, one of the main roof instability mechanisms in longwall mines. One alternative modeling technique is the UDEC Bonded Block Method (BBM) where bedded roof and support interactions can be explicitly captured. This paper presents the development of a BBM model of a longwall entry at a 180 m depth of cover with a three-entry gateroad layout along with roof extensometer monitoring results. The models are validated against the monitoring data, showing the potential for BBM numerical models capturing the complex roof and support system interactions to assist with optimizing gateroad layouts and support systems.

By JÖRG DEHNERT, PETER WINDISCH, Bernd Schönherrt, JENS STOPP

The Quick-Erect Stopping System (QESS) offers a new way of reducing the radon exposures of miners in Germany, especially during remediation work in old mines. The QESS is a light-weight, modular, and reusable construction kit of interlocking telescopic aluminum tubes, radon-proof foil, and expanding foam. It is designed to seal off radon-rich parts of galleries within only a few minutes. Originally, the QESS was developed to protect miners against radon exposures. Then, the QESS found the attention of several mine rescue teams at a German mining conference. The Student Mine Rescue of the Technical University Bergakademie Freiberg and the Wismut Mine Rescue carried out firstmine rescue drills in Freiberg and Schlema. Additionally, a mine rescue drill was carried out by the Front Range Mine Rescue in the Edgar Experimental Mine of the Colorado School of Mines. These drills helped to improve the systemand highlighted its potential for mine rescue operations. Now, the QESS is wellsuited for small-scale mining. The QESS can be used to seal off galleries in only a few minutes to both protect miners fromradon exposures and to support mine rescue operations. Moreover, the QESS was also successfully used in ventilation experiments.

Jul 23, 2020

By J. R. Thoenen

This circular is part 3 of the third paper (entitled "Excavation") of a series summarizing the technical problem; involved in the production and preparation of sand and gravel. Part 1 discussed the use of power shovels, draglines, and excavator cranes. Fart 2 discussed the use of power scrapers, slackline cableway excavators, and hydraulic monitors. This circular discusses the use of the hydraulic, clamshell, ladder, and dipper dredge. Part 4 to follow will discus the use of haulage equipment, and subsequent parts will discuss the application of both excavating and haulage equipment to various types of deposits. HYDRAULIC DREDGE Judged by the number of installations and the tonnage produced, as recorded in part 1 of this circular, the hydraulic or pump dredge is the most popular type of underwater sand and gravel excavator.

Jan 1, 1935

By W. H. Oppelt

Two exploratory gasification tests of limited duration were made at Dorsten, Germany, with strongly coking Pittsburgh-bed coal in a fixed-bed pressure gasifier. To reduce the coking potential of the Arkwright coal, ash refuse from the gasification of Dorsten (Leopold) coal was added to pre-pare coal-ash mixtures which contained nominal 20 and 30 percent ash. Major adjustments in principal process variables at the beginning of the tests resulted in wide fluctuations in the rate of gas production, gas offtake temperature, and carbon dioxide concentration in the gas. Because a higher steam-to-oxygen ratio was used in the tests than was customarily employed for routine operation, gas production was lower, and steam and oxygen consumption was higher. After operating conditions had been improved, the results of a 12~-hour-long test with addition of sufficient ash refuse to obtain a nominal 30 percent ash concentration indicated that operation is feasible with this coal mixture using a fixed-bed pressure gasifier equipped with a rotating coal distributor and stirrer.

Jan 1, 1966

By A R. Bye

The mining industry is facing some key challenges that provide a compelling case for geometallurgy initiatives. Over the last 30 years, the average grade of Australian orebodies being mined has halved while the waste removed to access the minerals has more than doubled. In the last eight years, the industry’s energy consumption has increased 70 per cent while multi-factored productivity has fallen 24 per cent. The paper documents a broad range of industry case studies which demonstrate strategies for gaining value from geometallurgy.The mining industry constantly faces the key questions of how significant ore variability is on mine valuation and how would knowledge of the variability change the mining schedule, mine to mill design and operation. Using case studies the paper describes the methods used for incorporating mineral extraction attributes into orebody models and their technical integration into daily operation as well as mine planning optimisation. While pit optimisation from a fully attributed geometallurgical model highlights areas of opportunity and risk it is shown that during the scheduling phase of mine planning that significant value can be added. The benefits from these projects included reducing geotechnical and environmental risk, improving mine to mill performance, option analysis and quantified cash flow risk. There is growing acceptance within the minerals industry that ‘realistically assumed modifying factors’ defined by a competent person/s are not sufficient to mitigate the risk of funding mining ventures. Geometallurgy is moving away from factored ore reserves to data-rich block models providing reliable information for mining, metallurgical and environmental considerations.

Sep 5, 2011

By J. N. Sicking, F. H. Brinkman

A new method for obtaining equilibrium vaporization ratios (K-values) for reservoir fluids has been developed and tested. By application of the method, complex experimental measurements of liquid and vapor phase compositions are eliminated. This simplified technique reduces the cost of experimental equilibrium-ratio data for reservoir studies of condensates and volatile crude-oil systems. The method is designed for systems of constant composition and, therefore, is best suited for depletion studies where compositional changes at high pressures are minor. The basic data required, in addition to the composition of the initial reservoir fluid, are the relative vapor-liquid volumes and densities at reservoir temperature and variom reservoir pressures. Tests demonstrated that the method predicts equilibrium ratios accurately for condensates. A single test on a crude oil was not conclusive; further testing will be necessary before the accuracy of the method can be determined for crude-oil systems. In addition to determining equilibrium ratios, the calculation method provides information on the physical properties of the "plus" component in the vapor and liquid phases. The "plus" component is that mixture of components heavier than the least volatile fraction analyzed. This information is useful in studies of both natural depletion and cycling operations for condensate reservoirs where the heptanes-plus component in the gas phase is produced from the reservoir. INTRODUCTION As more volatile oil and condensate reservoirs are found, the use of phase behavior techniques to predict their performance is increasing in importance. These techniques have long been used for condensate fields and have more recently been applied to crude-oil fields containing oils of medium-to-high volatility. In these phase behavior methods, equilibrium ratios (K-values) are used to predict compositional changes in the reservoir fluids—thereby accounting for the recoverable oil that exists in the gas phase. The reliability of the predictions depends to a large extent on the equilibrium ratios used. These values must be obtained for each component for the entire pressure range being investigated. Unfortunately, because of the complex nature of hydrocarbon mixtures, accurate K-values are hard to obtain. The equilibrium ratios for a particular component will vary not only with the temperature and pressure, but also with over-all composition of the system. The importance of composition is quite critical at elevated pressures, but becomes negligible at pressures below about 300 psia. Therefore, because most phase behavior problems involve the high-pressure region, each fluid system becomes a special case. Experimental programs to determine characteristic K-values are quite difficult and time-consuming. Thus, it is often necessary to resort to approximations of the K-value data. Charts giving K-values for various mixtures and classes of mixtures are available in the literature. However, there are two major difficulties in using them: (1) the K-values of the "plus" component (that mixture of components heavier than the last one analyzed) must be obtained by extrapolation from the K-values of the other components; and (2) the K-values obtained must finally be adjusted by trial and error to agree with observed volumetric data. To eliminate these difficulties, a new method of determining equilibrium ratios was developed. Briefly, after the composition of the system as a whole has been analyzed, the method uses empirical correlations and the gross fluid properties of the system (relative vapor-liquid volumes and densities) to calculate K-values. Because the calculative procedure is long, it is best solved on a digital computer. About one hour of machine time on an IBM 650 computer is required to develop a K-chart for the fluid being examined. DEVELOPMENT OF THE METHOD OF OBTAINING K-VALUES Equilibrium ratios are defined as the ratio of the mole fraction of a component in the vapor phase to its mole fraction in the liquid phase. This statement is expressed in Eq. 1. A typical plot of equilibrium ratios for a particular system is shown in Fig. 1. It should be noted that, at pressures near the saturation pressure, the K-values appear to converge to a common point. This apparent convergence point is called the convergence pressure and is a characteristic of the system involved. Various empirical correlations of K-values have been noted. It has been observed that an isothermal plot of