Search Documents

By K. E. Brown, J. P. Brill, A. R. Hagedorn, T. C. Doerr

A recent correlation for multiphase vertical flow by Hagedorn and Brown1,7 has been used to examine the effect of numerous variables such as pipe size, gas-liquid ratio, liquid flow rate, liquid viscosity, liquid surface tension, oil API gravity, water cut, etc., on flowing pressure gradients. Most previous correlations were derived by using a form of the general energy equation which assumed negligible changes in kinetic energy. Under certain flow conditions this can lead to serious errors in predicting pressure traverses. Examples of traverses calculated both with and without the kinetic energy term are included here. The Chew and Connully correlation for calculating changes in viscosity with changing pressure and temperature has been extended so that the effect of a changing viscosity with depth on pressure gradients can also be predicted. Examples illustrating the effect of tubing size show the importance of this correlation in determining pipe sizes for initial well completions. Limitations on production rates in small pipe sizes from excessive friction losses can be predicted with greater accuracy. The combined use of a vertical-flow correlation with a horizontal-flow correlation provides a method for determining the maximum flow rate possible from both flowing and gas-lift wells. Examples are included to illustrate application of the combined use of vertical and horizontal-flow correlations in optimizing production rates and minimizing excessive costs from over injection of gas in gas-lift wells. INTRODUCTION The problems of multiphase vertical and horizontal flow are immediately encountered in any producing well. Fig. 1' shows three stages of production: flow in porous medium, vertical flow and horizontal flow. All three stages affect the production rate from a well. If we are confronted with a particular well and consider only the variables involved in the vertical and horizontal stages of Fig. 1, we should be capable of calculating the flowing bottom-hole pressure necessary to produce a particular flow rate. A change in any of the variables results in a new solution to the problem. Recent approaches in developing horizontal and vertical-flow correlations have improved to the extent that the solution can now be obtained with more confidence than previously. VERTICAL AND HORIZONTAL FLOW CORRELATIONS Since Poettmann and Carpenter's' original work in multiphase vertical flow, there have been many additional vertical-flow correlations developed which have greatly improved the accuracy of pressure-loss calculations. These

Jan 1, 1967

By Paul D. Martinka

Coal is the principal energy source for the American Electric Power System (AEP System), which generates and delivers more electric energy to its customers within a seven-state area than any other investor- owned electric public utility. The company expected to burn 21.5 million tons of coal in 1968 at its coal-fired, steam-electric generating stations. About 4.3 million tons, representing 20% of the firm's total annual requirement, was the expected yield of its captive coal mines; the other 17.2 million tons were to be purchased from commercial mines in Ohio, West Virginia, Virginia, Kentucky, Indiana, and Illinois. American Electric's largest captive coal mining operation is conducted by Central Ohio Coal Co., a subsidiary of Ohio Power Co., at the Muskingum mine in the Meigs Creek No. 9 coal field of southeastern Ohio. The mine was started in 1953 to produce the coal requirements of the Philo and Muskingum River generating plants of Ohio Power Co., and it has been supplying their annual requirements in the range of 2.5 to 3.5 million tons since that time. The Muskingum River plant is one of the major steam-electric generating stations on the AEP System. This plant began operation in 1953 with a 215-megawatt unit and now has five generating units with a total plant capacity of 1,495 megawatts. The addition of the 615-megawatt Unit 5 in the summer of 1968 increased the total annual coal requirement of the plant from 2.6 to 4.4 million tons. In order to produce the additional 1.8 million tons of coal for the Unit 5 addition and to exploit the remaining coal reserves at the Muskingum mine most economically, Central Ohio Coal Co. has undertaken a $41 million expansion and modernization program, involving the world's largest dragline and an electric railroad.

Jan 1, 1969

By C. F. Cornell, R. C. Emmett, D. A. Dahlstrom

FOR many years the disk-type and cloth-covered drum filters have found widest application in liquid-solids separation, which uses continuous filters. The disk type is less expensive, occupies less floor space per square foot of filtration area, and requires negligible down time for filter media changing. However, because filter cloth is billowed out by the blowback in the cake discharge, it is very short-lived if the scraper blades are set too close. Consequently cake weight is very important in assisting cake discharge, which normally necessitates a minimum cake thickness of 3/8 to ½ in. Also, the vertical position of the disks eliminates the possibility of efficient cake washing for removal of soluble values. The disk-type filter is generally limited, therefore, to applications that require no cake washing and form relatively thick cakes within the normal range of filter cycle times. The conventional cloth-covered drum filter is a more flexible unit, permitting wider variation in the percentage of cycle time devoted to cake formation, dewatering, or washing, as required by the application. Thinner filter cakes can be discharged because a horizontal line across the filter medium at the location of the scraper blade is equidistant from the edge of the blade at all points. The scraper blade therefore may be set a short distance from the filter medium or, where wire winding is not used, a floating scraper can be utilized so that the contour of the cloth can be followed. The drum filter is generally employed when there are difficult filtering slurries with resultant thin cakes or when cake washing to recover soluble values must be practiced. Difficulties sometimes encountered in continuous filter operation can be summarized in the following four categories: 1) Low filtration and/or washing rates due to blinding of the filter medium. 2) Poor cake discharge resulting from sticky cakes, filter medium blinding, or too thin a cake for the particular type of filter. 3) High filter media costs caused by short life and frequent down times for cloth changing. This results from blinding or from abrasion by the scraper blade when cakes are thin. 4) Blowback of filtrate at cake discharge because not enough air passes through the cake to purge the drainage area and filtrate lines during dewatering. To reduce or eliminate blinding tendencies several modifications have been tried, for example, cover-cleaning showers, blowback under the feed slurry, and snap-blow cake discharge. In many cases, however, this simply retards the rate of blinding, since the filter medium is kept clean at its outer surface only by these methods. As blinding usually occurs within or on the back of the medium, the operator is finally forced either to remove the cloth and scrub the medium intensively with a cleaning solution or acid-rinse it on the filter—all resulting in down time, short cloth life, and additional costs.

Jan 1, 1959

By Lucien Eaton

THE use of filling in mines is less common in the United States than it is in Europe, where in some places it is required by law. In most cases the filling is placed by hand, and the material used for this purpose is the waste from development and that sorted from the ore in the stopes. When these sources provide an insufficient supply, additional rock must be quarried on surface or mined underground, or some other material :st be used. In different parts of the world sand, clay, gravel, culm, nulated slag, mill tailings, and even ashes, have been used as filling material in place of or in conjunction with rock. Of all the materials used for filling the best is probably clean sand. Gravel, finely crushed rock, granulated slag and coarse mill tailings are almost as good, and the methods used for placing and confining sand will apply equally well to any of these. The advantages of sand are its comparatively slight compressibility and the ease, economy and convenience with which it may be placed. On account of the voids, which necessarily occur in fills made of coarse waste, such fills will compress 10 to 25 per cent before they develop their full strength, whereas clean sand seldom compresses more than 5 per cent. Sand is especially desirable when practically complete filling is required, and sand derived from mill tailings, especially when not thoroughly cleaned, has been remarkably effective in sealing off and extinguishing mine fires. When natural sand is available on surface, or when it can be obtained from the mill tailings or tailings dump, the cost of using this material for fill will probably be considerably less than that of rock. In this paper it is not proposed to discuss all methods of filling, butt to describe some of the methods used for placing sand fill and to make a brief comparison of their merits.

Jan 1, 1932

By Paul M. Tyler

NOW that the dust of World War II has settled and we and our allies are faced with extravagant losses of men, money, and materials, virtually the only hope that the United States and Britain have in the way of reparations lies in the capture of industrial, technical, and scientific secrets. Even during the war American and British scientists and technicians gained access to German factories, questioned German personnel, studied German documents, and endeavored generally to keep pace with new discoveries in science, industrial technology, and process development. Under various agencies this work continued for two years after the war. Altogether at least 600 American scientists and industrialists have gone to Germany and brought back reports and several times as many British, Canadian, and. Australian investigators have been similarly engaged under co-operative arrangements designed to assure the maximum of coverage with a minimum duplication of effort. As a result of these investigations and document studies, about 500 or 600 reports have been prepared on metallurgical and allied subjects. Those by American authors or joint teams have been listed in the annotated Bibliography of Scientific and Industrial Reports, issued by the Office of Technical Services in the U. S. Department of Commerce. Many of the British reports are also available in this country through the same office or through a British representative in New York. Since it was my duty to read most of these reports for

Jan 1, 1948

How Mining Engineers Will Fare in 1977 Mining Education- The State of the Discipline Coal Mining Technologists are a New Force in the Labor Pool Trained Manpower Provided by Mining Technology Programs Putting New Engineers to Work-A Management Perspective

Jan 1, 1977

By Charles Hart

In this paper it is the author's intention to show the extent and character of foreign ores now known to be available; these deposits may be in active production or held in reserve until economic conditions may make them active. He hopes to show the relation existing between these ores and the American supply, and which of the former are now producing or will in turn come into production when our better ores have been exhausted. This phase of this discussion must of necessity include some data as to the present rate of consumption and a study of the changes we may expect here and abroad in the general steel trade and its sources of supply in raw materials. It is obvious that the occurrence of coal, ore and limestone in relation to one another and the proximity of a market are the elements in control of this feature of the problem. If the foregoing situation is favorable, all the other questions may be solved, for it is clear that with proper basic conditions finance, labor and operations will fall in line. We present a short outline of the present methods of carrying on the foreign iron ore trade, believing that it is of general interest in comparison with our own highly specialized methods, and that with the exhaustion of our better ores we will be compelled to seek a part of our supply abroad. A partial list of iron ores, with incomplete analyses (Table I), is added, to give a better understanding of the general situation and explain to some extent the reason for things being as they are in the iron and steel trade of the world and to help in bringing this paper to an informing conclusion. The question of the world supply of iron ores has been a subject for study on the part of geologists and engineers for many years, and found its best results in the Eleventh International Geological Congress, appropriately held at Stockholm, Sweden, in 1910. The proceedings are published in two volumes and are undoubtedly the best records available on this subject at the date of publication. It should be borne in mind, however, that much has happened in the 20 years since these figures were assembled. There is just as much known ore at present as at that time, minus the quantity consumed, plus newly discovered reserves. The World War had great effect upon this situation; during that time explorations were greatly reduced and the settlements after the

Jan 1, 1929

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contamination could be reduced about 80 pct. The water company's supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters, and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West P~M Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs sup- plying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical "Coal Measures"

Jan 1, 1949

By P. Somasundaran, D. W. Fuerstenau

This article presents the results of an analysis of grinding of 1:1 mixtures of 4x8-mesh quartz and limestone in laboratory ball and rod mills. From these experiments, the amount of energy consumed in grinding each component of the mixture was determined. In the ball mill, limestone consumes slightly more energy than quartz in the initial stages of grinding, but as the grinding proceeds quartz begins to consume a slightly greater fraction of the energy. The postulate that the fraction of energy consumed by any material in a ball mill is proportional to its volume fraction has been shown to be approximately true. On the other hand, in a rod mill energy consumption by quartz and limestone is equal only in the initial stages of grinding, with energy consumption by quartz greatly exceeding that by limestone as rod milling proceeds. Preferential energy consumption in tumbling mills has been discussed in a number of papers. For example, from an analysis of the kinetics of comminu- tion in ball mills, Arbiter and Bhrany' obtained rate equations based on the postulate that only coarse particles are ground, indicating that fine particles are protected from the action of the balls by coarser particles. In rod mills this protective action is much more pronounced than in ball mills. Recent studies on the rod milling of limestone-quartz mixtures have shown that this protective action causes the mineral with the lowest grindability (quartz in this instance) to consume the greater fraction of energy. 2 However, in the ball milling of mixtures it has been postulated that the consumption of energy by one of the constituents is determined by its volume fraction within the mill. 3 Possibly this hypothesis may be a simplification of the ball milling of mixtures since the protective action suggested by Arbiter and Bhrany may result in some preferential energy consumption by one of the constituents of a mixture. The objective of this study has been to determine preferential energy consumption in laboratory ball and rod mills by analyzing size distributions of each material in the products obtained from grinding 1:l mixtures of quartz and limestone. MATERIALS AND METHOD The procedure for carrying out the tests on wet grinding quartz-limestone mixtures has already been described.'r3 In the present investigation, 1:l mix-

Jan 1, 1963

By AIME AIME

ON MAY 22 the American Institute of Mining and Metallurgical Engineers will commemorate the sixtieth anniversary of its founding at Wilkes- Barre, Pa., in May, 1871. The Directors have transferred the May meeting of the Board to Wilkes-Barre, and the Pennsylvania Anthracite Section has invited as many members of the Institute as can to be present at this time and to join with their fellow-engineers at Wilkes-Barre in the inspection trip through a portion of the anthracite district that has been planned. Ac- cess to Wilkes-Barre is easy, from nearby points, over excellent automobile roads, or by train. The distance from New York is only about 140 miles. , It is hoped to engage a special car for those travelling by train from New York, which will leave the Pennsylvania Station over the Lehigh Valley Railroad at 11:50 p.m., arriving in Wilkes-Barre the next morning. Return can be made from Wilkes-Barre by sleeper the same evening, arriving in New York Saturday morning. Other trains are available for those who prefer a daylight journey.

Jan 1, 1931

By A. B. Parsons

Jan 1, 1971

By Robert B. Fulton

The use of industrial minerals by the chemical industry as raw materials for manufacturing and in processing spans a wide assortment of minerals. This chapter aims to supplement rather than duplicate the commodity chapters. Its objective, to describe the uses of industrial minerals in the manufacture of chemicals, is attained by considering minerals used by the chemical industry in terms of the chemical element required and by giving particular emphasis to market factors. The mineral aspect, which is covered in the commodity chapters, is subordinated and attention is focused on the chemical and market aspects. Condensing this broad subject into a few pages permits treating only the most important elements derived from industrial minerals. The elements derived from petroleum, hydrogen and carbon, which quantitatively dominate as raw materials for the chemical industry, are omitted, as are the metallic elements and the minerals covered in other "use" chapters such as phosphorous, potash, and nitrogen for fertilizers and titanium dioxide for pigments. After eliminating on this basis, our definition leaves six elements of major importance: boron, bromine, chlorine, fluorine, sodium, and sulfur. These elements are treated individually under separate headings. Salt brines have particular importance as raw material sources for the chemical industry as shown in Table 1 "Salt Brine Derivatives" (Anon., 1967), which charts the chemical compounds derived from four types of brines: (1) Owens Lake type brines which are sources of boron and sodium compounds; (2) Midland type brines from which bromine, iodine, and chlorides of calcium, magnesium, potassium, and sodium are derived; (3) Searles Lake type yielding boron, bromine, lithium, magnesium, potassium, and sodium compounds; and (4) Silver Peak type produced mainly for lithium. Table 2 (Jones, 1973) affords an overview of the chief industrial minerals, the chemical products derived from them, and end uses of the products.

Jan 1, 1975

THE annual meeting of the Lake Superior Mining Institute was held on Sept. 7 and 8, Crystal Falls and Iron Mountain, Mich., being the principal centers of activity. Members of both institutes began assembling early, and by the evening of Sept. 6, some 60 had already arrived at Crystal Falls. The greater number arrived the following morning, however, and after the usual formalities of registration were attended to, the party were loaded into automobiles and set out on a tour of inspection of the mines near Iron River; some properties were passed through, and some were briefly visited to permit the inspection of any unusually interesting piece of equipment or detail of practice. The last stop of the morning was at the Caspian, Iron River, where the entire party was entertained at luncheon at the Caspian Club House. Both the food and the company were excellent, and as the weather was superlatively good (though the natives of the district modestly declared it was only ordinary autumn weather) the lunch was served on the lawn at the rear of the club, where the green turf, abundant flowers, and music by the band, added to the charm of good fellowship. The degree to which mining men have become addicted to golf was indicated by the large number of plus fours in evidence, whose wearers appeared just before lunch and disappeared immediately afterward.

Jan 1, 1928

Jan 1, 1884

By L. B. Slichter

Prospecting is certainly the world's biggest and best gambling business. It is a game where the chips cost many thousands and where many millions, even billions, can be won. An attractive feature of this gamble is the fact that the players are free to rig the odds as favorably as possible. Only the limited bounty of nature, the restrictions of the laws of the land, the competition from other players, the limited sagacity of the player himself— only these, and other factors, restrict the possibilities for large winnings. Today probably about half the land surface of the earth remains to be searched for signs of ore visible at the surface. It is fortunate that so much land still remains for exploration by relatively economical methods. Looking to the future, it is a good guess that the costs of finding ore will increase in response to increasing technical difficulties. To continue to achieve profits from prospecting, it will become necessary to analyze the business more skillfully, in a more and more sophisticated manner. Whenever feasible, qualitative concepts must be replaced by their quantitative equivalents, improvements, and extensions. THE GAMBLE The fact that prospecting is a gambling business reminds us at once of the elementary rule known as the law of gambler's ruin. I hesitate to mention so simple a rule in this company of experts. This rule expresses the rather serious chance of going broke when the odds for success are small, merely by a normal run of bad luck regardless of the long-run expectations of gain. The only sure way of avoiding this special risk of gambler's ruin is to have enough capital, and the will, to continue the play many times and thus ride out the inevitable runs of bad luck. For example, if the probability of success is one in ten for each venture, there is a 35 pct chance that ten successive ventures will fail in a row. But if one has the capital to continue the play through a run of 100 failures, then the chance of gambler's ruin is only 5 in 100,000. Almost any management, I suppose, would be under terrific pressure to cease the play during a long run of bad luck. To continue to prospect under such circumstances requires great confidence in the premises, and a firm conviction in the long-term expectation of profit. There is evidence which I shall mention that in the future even the strongest companies may not have the necessary capital to prospect on the ideal scale. Joint ventures will be very desirable as a means for extending the available venture

Jan 1, 1961

By A. A. Stripling

The Cretaceous limestone wells of the Mara/Maru-caibo Dist. of Venezuela are extremely prolific producers. To maintain production on cessation of natural flow, large scale gas-lift operations were commenced involving high production rates on caring Flow. For the design of these gas-lift installations it was essential to have some knowledge of the pressure gradients involved in casing flow, so that the required injection pressures, optimum gas injection raws, etc., could be forecast. This paper presents a method of calculating these annular pressure gradients. Basically the method makes use of an energy balance equation coupled with an empirical energy loss factor derived from field data. The calculations have been put in a form suitable for "punch card-type" calculating machines. A set of gradient curves for Mara/Maracaibo conditions covering flow rates up to 12,000 B/D, and GOR's of 500 to 2,000 cu fd/bbl is presented. From these curves the flowing BHP can be predicted from surface data and the vertical pow performance under varying conditions of gas injection can be estimated. The method has been applied to La Paz and Mam gas-lift operations for over three years and has given consistently accurate results. INTRODUCTION The Cretaceous limestone fields of the Mara/Maracaibo area in Venezuela are characterized by the presence of widely distributed fissure systems. Under these conditions individual wells frequently have extremely high potentials and such wells are generally flowed on the casing-tubing annulus in order to reduce the pressure loss in vertical flow. To maintain production on cessation of natural flow, an extensive gas-lift system was planned. As a first approach to this gas-lift design problem, an attempt was made to construct a set of empirical flowing gradient curves from the available subsurface pressure data. Such a method has been used successfully for tubing-flow conditions in California by Gilbert'. Unfortunately, the empirical construction of casing-flow gradient curves presents additional difficulties, as pres- sure bombs cannot bc run in the casing-tubing annulus against high rates of flow. Thus, the Full flowing gradients cannot be defined by actual measurement and the best that can be done is to obtain spot pressures at the tubing shoe. Under these conditions a vast accumulation of BHP data is required to construct a set of gradients. To the La Paz and Mara fields the majority of the available flowing pressure measurements fall into a relatively narrow GOR range, in the neighborhood of the solution ratio. While there appeared to be reasonable prospects of constructing gradient curves for this limited range, measurements at higher GOR's, which were of major interest for gas-lift operations, were relatively few and the prospects of constructing empirical curves cor~spondingly remote. As an alternative approach, the possibilities of a mathematical analysis of vertical flow conditions were investigated. May and Laird2fV n 1934 presented an excellent analysis of the vertical-flow conditions in the Anglo-Iranian Oil Co.'s fields. Their analysis was based on an energy-balance equation and calculated the losses due to kinetic energy, friction and slippage separately. By combining these losses with the total calculated available energy, the required depth-pressure traverse could be deduced. On applying the method to La Paz conditions, good results were obtained for tubing flow at high tubing-head pressures. However, for lower wellhead pressures (300 psi and under) the discrepancy between calculated and measured values increased appreciably. It was considered that this was probably due to energy losses caused by slippage or liquid hang-up in a continuous gas phase, for which it was difficult to visualize any analytical approach. In 1952 Poettmann and Carpenter4 presented a method of pressure gradient calculation which, while based on an energy-balance equation similar to that employed by May and Laird, made no attempt to evaluate the various components making up the total energy loss resulting from irreversibilities of flowing fluids. Instead, they proposed a method of analysis which assumed that all significant losses for multiphase flow could be correlated in a form similar to that of the Fanning equation for frictional losses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The total available

Jan 1, 1881

By A. N. Holden, W. E. Seymour

DURING the last several years, the U-Zr system has been studied at many laboratories as one of the research programs sponsored by the Atomic Energy Commission. The equilibria in part of this system have been difficult to determine, although the phase diagram from 0 to 60 atomic pct Zr has been established with reasonable certainty. Existing diagrams of the system vary appreciably beyond 60 atomic pct Zr, particularly with regard to the existence of an intermediate phase. Most existing diagrams show a transformation or reaction horizontal near 600°C. In 1955, a collection of uranium phase diagrams' was prepared at the Battelle Memorial Institute and the U-Zr diagram in that collection contained a questionable region in the vicinity of 60 to 80 atomic pct Zr. Summer-Smith" has published a phase diagram of the system that shows no intermediate phase. Summer-Smith did his work with powders and found only the uranium and zirconium eutectoid mixture from X-ray patterns of material annealed below 600°C. Mueller3 at Argonne National Laboratory did similar work with filings, and he found that initially there was a pattern of an intermediate phase, but on long-time annealing

Jan 1, 1957

By Phillip E. Deering, Robert M. Cox

A model pillar study was conducted in which the engineering principles of dimensional analysis were applied to the problem of coal mine pillar design. The paper reviews the theory of similitude as applied to the model pillar study conducted in the investigation. An example solution of a design problem is included to indicate how the results of the study may be used as a first approximation in the design of coal mine pillars. The design of mine pillars for adequate support with minimum loss of valuable raw materials has always presented a problem to the mining engineer. Most often, for lack of a better method, past practice has influenced the design of new mine pillars. This process has always left doubt as to the safety factor of the pillars. The work presented in this paper is an initial attempt toward adapting the engineering principles of dimensional analysis to the problem of pillar design in underground mines. The use of the dimensional analysis technique is advantageous because all the variables associated with the problem are considered, and by systematic analysis the relative influence of each variable is determined. The model material utilized in this study was taken from the Helena seam of the Cahaba coal field located in central Alabama. The research study was sponsored by The Southern Electric Generating Co. as part of an over-all rock mechanics investigation of the Helena seam area. THEORY OF SIMILITUDE Model analysis is used extensively in engineering today, particularly in the solution of design problems that defy the classical methods of analysis. Such problems arise when materials with a nonlinear stress-strain relationship are involved, when geo- metric boundaries are difficult to define in simple form, when strains become large, or when partial failure occurs. All of these difficulties usually exist in pillar design problems. Those principles which underlie proper design and construction of models, and the interpretation of test results, comprise the theory of similitude. That is, the theory of similitude includes a consideration of the conditions under which the behavior of two separate entities or systems will be similar, and the techniques of accurately predicting behavior of one from observation of the other. The theory of similitude may be developed by dimensional analysis. Dimensional analysis, as a powerful analytical tool, is developed from a consideration of the dimensions in which each of the important quantities involved in a phenomenon is expressed. It is based on two axioms: 1) Absolute numerical equality of quantities may exist only when the quantities are similar qualitatively. 2) The ratio of the magnitudes of two like quantities are dependent on the units used in their measurement, provided that the same units are used for evaluating each. Dimensional analysis, developed from these two axioms, differs from other types of analysis in that it is based solely on the relationships that must exist among the pertinent variables because of their dimensions, rather than on the relationship of natural laws. In itself, dimensional analysis ~rovides qualitative, rather than quantitative relationships, but when it is combined with experimental procedures, it may be made to supply quantitative results and accurate prediction equations. APPLICATION OF THEORY The design of an adequate mine pillar requires the determination of a design equation and the selection of a dimensional system with which to work. Since force plays an important part in the design of mine support, the FLT (force, length, time) system has been used. The factors involved in the dimensional analysis of mine pillars and their dimensions are: A = cross-sectional area L Cp = design strength FL- E, = tangent modulus of elasticity FL

Jan 1, 1969

By H. J. Gerritsen

From presently available components a portable, rugged, reliable apparatus can be built which will be able to detect methane concentrations of 0.1% and lower in air. Sensitivity and design considerations of the apparatus are given. Ways to build even simpler and cheaper apparatus in the future are indicated. Traditionally the problem of detecting and monitoring the presence of dangerous gases present in small concentrations in air has been a difficult one. Whether canaries,' or sophisticated chemical or thermal conductivity methods are used, they seem to be either slow, cumbersome, or otherwise not completely satis factory. A seemingly natural way of gas detection is to measure the strength of absorption undergone by light of a wavelength that the gas to be detected absorbs. This method has been difficult to apply in view of the low power output over a narrow wavelength range in the infrared from traditional glow bar light sources. Besides, the apparatus to select such a narrow band of wavelengths is quite costly and complex. The use of a laser solves these problems simultaneously. Although a variety of lasers are available to detect a variety of gases (such as carbon monoxide or methane) whose early detection would be desirable, this paper deals exclusively with the use of lasers for methane detection. ABSORPTION SPECTRUM OF METHANE IN AIR The absorption spectrum of pure methane is very well known.2-4 There are four fundamental vibrations, all occurring in the infrared of which only two absorb strongly. They occur at 3.3 µ and 7.7 µ. The absorption spectrum is quite complicated due to the fact that the methane molecule can rotate in a variety of rotational quantum states. These rotational states are furthermore split by anharmonic forces such as the Coriolis force.4 When methane is present in air at atmospheric pressure, much of the very fine structure due to the anharmonic force is washed out since the pressure broadening is of the same magnitude as the splitting due to anharmonicity. For most of the spectrum at 3.3 µ, the rotational lines are typically separated by 0.01µ while the individual linewidth is 0.0001 µ. It is thus very important that the laser emit at a wavelength that coincides with one of these rotational lines. Before elaborating on the point that such a laser exists and how it performs, it is necessary for later discussion to point out that in the

Jan 1, 1967