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By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By R. H. Wightman, C. D. Chandler, P. B. Nalle

SURFACE quarrying at the Crestmore Div. of Riverside Cement Co. in California was started in 1909. In the early 1920's it was considered that these deposits were nearly exhausted for the equipment available at that time, and in 1927 the company began a block caving system. This mine continued operating until February 1954. In 1941 trucks and crawler-mounted shovels had reached a stage of development that permitted reopening the quarries in conjunction with the underground mine. In 1948 surface reserves and the well developed limestone of the caving system neared depletion. To go deeper with the caving system was unattractive because of the economics, changes in physical structure of the rock at depth, and the perched water table

Jan 4, 1957

By L. W. Saperstein, W. B. Wells, L. B. Phelps

Several strip mine spoils are being examined to better understand their physical nature. The spoils were core drilled and each hole was logged using a nuclear geophysical tool to obtain bulk density data. Bulk density is an important property which provides insights into spoil porosity as well as other characteristics. The holes were drilled in spoils representing a variety of overburden removal methods, spoil ages, spoil depths, and area lithology. The relationship between bulk spoil density and mining method, spoil age, spoil depth, particle size, and lithotype is presented.

Jan 1, 1984

By Chester Purington

THE AUTHOR hopes that this paper will meet with criticism and debate by fellow members of the Institute rather than with that attitude of passiv-ity and indifference which one is inclined to adopt when considering a field completely foreign to one's own experi-ence. After several years of study of voluminous literature, maps, and statistics, and many personal journeys and field inspections of various parts of Siberia, the conclusion is reached .that the area adjacent to the Stanovoi, Zhugd-Zhur, and Yablonoi ranges as below defined is that which .is most accessible to the western world and will soonest give results from exploration. HISTORY The first incursion of the Russians into Siberia east of the Yenesei River appears to have been in 1632 when the fort of Yakutsk was founded on the middle Lena. The early expeditions were in quest of furs. As the Siberians say, "the sable beckoned" and the post of Anadyr was founded in 1639, two thousand miles further northeast. Thus nineteen years after the Pilgrims landed in Massachusetts, the Russians had established a trading post within 700 miles of what is now the town of Nome, Alaska. Parties of Cossaks penetrated to the shores of the Okotsk1 Sea early in the seventeenth century, but it was not until 1688 that the town of Okotsk was founded. In 1712 a grand project was elaborated at St. Petersburg for building a port at Okotsk, but it came to nothing. Vitus Bering, the Alaska explorer, built ships at Okotsk, and made this his point of depar-ture. It is stated that the iron work used in these ships was brought overland partly from Yakutsk, and partly even from St. Petersburg, 5500 miles away. Accord-ing to report a copper deposit was worked on the river Urak, not far from the coast, and copper was smelted for sheathing the bottoms. Grassgrown mounds con-taining slag and shots of copper were inspected by the writer last summer, at the site of the ancient shipyard.

Jan 11, 1923

By Howard Smith

FOR several years this Institute has recorded in its TRANSACTIONS the various discoveries of potash? in America, and the successive stages in the development of an independent domestic potash industry. This paper is intended primarily to continue the record through the year 1935. In retrospect it is not inappropriate to note that public interest aroused in 1910 resulted in the production of some 1090 tons of pure potash in 1915, as a small beginning in the domestic inorganic potash industry, and that the infant industry thus begun reaches its majority this year, following a record production in 1935 of about 600,000 tons of potash salts and exports to no less than 22 foreign countries, including six countries in Europe. This production, with an estimated 200,000 tons of pure potash, may be compared with a production in 1934 of 430,157 tons with an equivalent of 144,342 tons of pure potash.

Jan 1, 1936

During the year this Committee has had the benefit of the services of 75 Committee members, resident in the various States of the Union and in foreign countries, 10 of them representing us abroad. A number of plans for awakening the interest of possible new members have been carried out and the results have been very gratifying. The comparative results for 1913 and 1914 are as shown in the following table: 1913 1914 Applied for membership 630 946 Elected 450 1,006 Accepted election 433 921 When it is remembered that the depression following the outbreak of war in Europe has had more serious effect on the mining industry than almost any other, these results cannot be regarded as anything other than very encouraging. Because of the unsatisfactory conditions still prevailing it will doubtless be difficult to make even as good a showing next year. It is considered, however, that the function of this Committee is not merely to secure new members, having no regard for other than numbers; its true function is to exercise a proper supervision over the growth of the Institute, building it up in those fields in which it is weak, and directing its growth in such a way as to make it most effective in fulfilling its proper function as the national organization representative of the mining profession. The plan of inviting the alumni of the leading mining schools to apply for membership, which was initiated last year, was completed this year, with the exception of one or two schools, notably the University of California, from which we have not been able to obtain a list of alumni. With these exceptions we have now extended to the graduates of all the important mining schools of this country, and several of those abroad, an invitation to apply for membership in the Institute. It. is not thought desirable to repeat this invitation too frequently, and it is therefore suggested that this field be left alone for a year or two, when, if the mining industry experiences a marked revival of interest, it will be well to send out a second letter to the same men.

Jan 4, 1915

By Zhu Weishen, Xu Dongjun

In the 1st part of this paper a comparassion of the different methods for determining the modules of elasticity and deformation of hard rock is made. It is found that the plate bearing method has a serious shortcoming. The slit flat-jack method seems to be a mare reasonable technique, which is recommended as a desirable method for in situ testing. In the 2nd part, a new test method to determine the properties of deformation and strength of weak plane in rock mass is recommended. Then the relation of weak plane character to the character of stress-strain curve, the relation of normal stress to the character of shear displacement curve and the yielding criterion of weak plane are discussed.

Jan 1, 1982

By Arthur F. Colombo

The selective flocculation, desliming and flotation process developed by the U.S. Department of the Interior, Bureau of Mines, as part of its goal of maintaining an adequate supply of minerals to meet national economic and strategic needs is described. The application of the selective flocculation and cationic flotation process to three oxidized taconites from the western Mesabi Range in Minnesota is discussed. Data from the operation of a 408-kilogram-per-hour (900 lb/hr) pilot plant employing reclaimed water are summarized for the three types of oxidized taconites.

Jan 1, 1980

By Robert E. Wilson, J. K. Roberts

IN order to make clear the reasons for the basic importance of petroleum and natural gas in the world today, and the problems faced by our scientists and technologists in using efficiently these great natural resources and finding possible replacements for them, it will be necessary to present a brief discussion of hydrocarbon chemistry The most important use of petroleum products is as fuel, particularly for the various forms of the internal-combustion engine There are, of course, hundreds of thousands of chemical compounds that give off heat when they burn, that is, when they combine with the oxygen of the air If a capable chemist were assigned the problem of finding the ideal volatile liquid fuel for use in an engine, he would probably begin by referring to the tables that give the heats of combustion of the chemical elements Of all the ninety-odd elements, hydrogen shows up with by far the highest heat of combustion-about 52,000 British thermal units per pound Unfortunately, however, hydrogen is a very light gas, which can be liquefied only at very low temperatures To burn it as fuel in an automobile would require a balloon about as big as the car to hold the equivalent of a gallon of gasoline, or, the hydrogen could be compressed in heavy steel cylinders, but -this would require about 125 pounds of steel per pound of hydrogen. Obviously, then, hydrogen itself cannot be considered

Jan 1, 1947

Engineers and masters of enterprise are waking fast to the realization that there is something more in the relations of employer and employee than mechanical output, which can be measured mathematically, and that the human side of service must receive greater consideration for the future. So much has been said and written on this subject that it has passed into a truism. Should not the same element, long neglected, be considered as of even greater importance than questions of "administration and membership, in the plans of engineering societies? Should mutual service and interest end with mere technical output by members and the rendering of care and management by officers? The world is recognizing, as never before, obligations for service to fellowmen clue from all, high or low, in rank or wealth. Our technical societies, organized for professional protection and advancement, are, insensibly to themselves, almost without conscious intent, widening their field of service to members and dealing heartily with questions broader than technique. Those who are doing such service find unconsciously more and more satisfaction in work so rendered. The growth of knowledge that comes to subaltern engineers or veterans by converse and contact with their fellows, working along and versed in the same subjects, brings interest and friendship. In this way are built some of the warmest friendships of life, coming as incidental and pleasurable result of meetings undertaken for other purposes. Should not the friendly purpose, the desire for service one to another, and es-

Jan 1, 1919

By William Braden

IT is obvious that the choice of the method to be employed in the handling of blast-furnace slags and mattes depends upon local facilities and conditions which may indicate as advisable some particular plan. As a result of the variety of such conditions hardly any two smelters use identically the same method, though they be located only a few hundred feet apart. For instance, of the several plants in Leadville, Colorado, each has a more or less distinctive system. The same is true of Salt Lake City and vicinity. In view of this it is evident that the existing diversity of practice cannot be accepted, prima facia, as evidence

Jan 1, 1897

By V. P. Yashin

Modern trends in the use of autogenous grinding of minerals have been investigated by Mekhanobr Institute. The conclusions drawn are based on experimental and theoretical investigations by the author and his coworkers. A method is suggested for determining the efficiency of converting from ball milling to autogenous grinding. A qualitative interpretation is given for comminution theory using both methods. This interpretation is used as a basis for considering both the principal trends in increasing use of primary autogenous grinding and the results of such in industrial application. Data are given from testing some ores from USSR deposits for the effect of the ore Preparation step on subsequent metallurgical treatment. Autogenous grinding is shown to be widely used in various USSR industries.

Jan 1, 1980

By R. L. Loofbourow

The objectives of this report are (1) to indicate what is known of natural rock temperatures as deep as 5000 ft below the surface, (2) to indicate methods for estimating such temperatures in localities where directly measured temperatures are un- available, and (3) to outline as far as possible, areas in the 48 states within which rock temperatures are likely to be low and high. The usual object of temperature measurements in deep mines and wells is to learn the temperature of air or another circulating medium. This usually differs significantly from the undisturbed rock temperature. The subject is complicated further by the variety of the thermal properties and structures of rock masses, the migration of fluids within them, the diversity of the history of rock masses and of the processes which have been at work on them during that history.

Jan 1, 1966

By Richard Franchot

From an efficiency viewpoint, the greatest loss of energy to the blast furnace is in its failure to convert more than about a third of the coke carbon from carbon monoxide to carbon dioxide. This result has usually been ascribed to a necessity of a 2:1 excess of CO in order to reduce iron. It has, however, been proved that iron is completely reduced by equal volumes of carbon monoxide and carbon dioxide. Hence there is room for the hypothesis that vaporization, as cyanid, of accumulated alkalis is a serious primary factor limiting the ratio of ore to coke. Observed cyanid vapor concentrations and those measured by the variations of the nitrogen-oxygen ratio in the hearth gases form the basis for a quantitative explanation of the furnace action. As EVERYBODY knows, the blast furnace is a gas producer. As to the reason for this, people are not so well agreed. The significance of the fact is obvious, for the extent to which the fuel leaves the furnace as combustible gas measures poor economy in iron smelting; while good efficiency in this respect means poor gas. The furnace thus works at cross purposes. The present trend of the steel industry is toward. a primary use of the blast furnace as a gas producer with pig iron as a byproduct. Needless to say, this trend is away from improvement in iron making. The production of more and better iron in a given furnace consuming a given amount of coke would seem, at least, to involve a decrease in the relative proportion of the combustible gas. The possibility at the same time, however, of making more and better gas need not necessarily be excluded. (The more the furnace acts as gas producer, the bigger is the sulfur problem.) Whatever the object, it would seem desirable to have a, clear, comprehensive, mathematically exact estimate of why and how the blast furnace functions, to the large degree that it now does, as a gas producer. The literature does not give a definite answer to the question. That for which explanation is sought is the fact that only a minor part, usually not more than a third, of the coke carbon burned is oxidized to carbon dioxide; that the development in the furnace of the fuel energy is thus limited usually to little more than 50 per cent.; that it requires about twice as much fuel coke to make a ton of iron as is indicated by the rela-

Jan 7, 1925

By Charles R. Wilson, Thomas W. Doe, Jane C. S Long, Howard K. Endo

An approach to treating flow through fractured rocks is presented which involves (1) determining statistical distributions for fracture area, density, orientation, and aperture from field data, (2) computer generation of fracture systems from the statistical distributions, and (3) analysis of the permeability and porosity of the fracture systems. The fracture density and orientation data my come from core logging or mapping. The hydraulically appropriate apertures and areas of the fractures come from transient flow analyses of single fracture well tests. These tests my also yield information on fracture deformability. Analysis of flow through computer generated fracture systems shows that an equivalent porous medium permeability can be defined for some fracture systems if a large number of fractures is taken into account.

Jan 1, 1982

By John W. Brauns, David H. Orr

9.1-1. Description and Basic Function. A conventional railroad haulage system for a surface mine performs the function of transporting the ore and/or waste out of the pit to a crushing plant or dump. Trains consisting of a locomotive and gondola or side-dump care suitable for loading by power shovels are used. Gondola cars are restricted to hauling ore as a rotary dumper is required to unload them. Side-dump cars are more versa- tile, being satisfactory for carrying both ore and waste; but because of their additional dumping mechanism they are likely to be more expensive to maintain (12). Also they weigh up to two times as much as a flat-bottom car of the same capacity, and, therefore, fewer cars can be hauled per train. Standard-gauge track is most commonly used. Track systems incorporate temporary track of low quality in areas where moves are frequent and permanent track of high quality on main lines. Rail haulage enabled open pit mining to establish its reputation, for efficiency. Prior to World War II it was the principal type of transportation used in large pits. Other successful surface mine haulage methods have been developed since that time. These have served to supplement railroad transportation, permitting selection of a method that is best adapted to the peculiar requirements of each mining project. 9.1-2. General Applicability and Controlling Physical Conditions. For handling rough rock, the shovel-train system is unexcelled (6). The ideal application is in a physically large, but not excessively deep, open pit mine from which the coarsely blasted ore and waste must be transported distances in excess of three miles. If, in addition, a high production rate is to be maintained, railroad haulage will probably afford a lower cost per ton transported than will any other haulage method. Relatively gentle

Jan 1, 1968

By Peter Haasen

INDIUM antimonide has the zincblende structure. A possible defect that does not disturb the indium tetrahedron surrounding any antimony atom in this lattice (or vice versa) is obtained when neighboring

Jan 1, 1958

By Norman Visnes

EARLY in 1954, as initial development of the Galena mine was being finished, plans for stoping operations became the foremost consideration of the operating management. The Galena is being operated under lease agreement with the owner, Vulcan Silver-Lead Corp. Started in 1947, the Galena is a deep level development of American Smelting & Refining Co. and Day Mines Inc. under the management of ASARCO, in the Coeur d'Alene mining district. Lead mineralization was found on the 3000 level in 1950. In 1953 development on the 3000 level disclosed a siderite vein, later known as the Silver vein, which contains commercial quantities of silver in Tetrahedrite. This vein was explored on the 2800 and 2400 levels and later on the 3400 level, the lowest in the mine. Work above the 2400 level to date has indicated that the vein dissipates to weak mineralization, and ore values are uncertain above the 2200 horizon.

Jan 1, 1957

By William S. Hannan, H. Rush Spedden

Flotation may be defined as a process whereby mineral particles are concentrated by selective adhesion to air-liquid interfaces. The process involves attachment of desired mineral particles to air bubbles, and removal of the mineralized air bubbles from the surface of the pulp as a mineral concentrate. Problem Although great strides have been made in understanding the principles of flotation, one part of the process which has not been adequately explained is the mechanism by which selected mineral particles become attached to air bubbles. A glance at the froth of an operating flotation cell demonstrates adequately that use of proper reagents and conditions mill result in such attachments; but how such attachment takes place is not definitely known. A better knowledge of this factor might lead to improved flotation practice either through altered machine design or the application of scientific innovations. Direct observation of the behavior of mineral particles and bubbles in an operating cell does not appear promising because of the complexity of the system. For this reason, conclusions concerning the problem must be deduced from theoretical considerations or from observation of simplified systems designed to reproduce conditions thought to exist in an operating cell. Present Theories Two mechanisms have been recognized as fundamental in particle-bubble attachment: gas precipitation and direct encounter. It is a simple matter to demonstrate in the laboratory that attachment can be brought about by either mechanism. As to the relative importance of the two in a particular flotation system, however, there is a divergence of views. Taggart1 states, Under exceptional circumstances sufficient force and time to effect attachment may conjoin in an ore pulp undergoing agitation, and a preformed bubble adhere to a collector-coated mineral particle, but the occurrence is rare. . . . Pulp-body froth flotation effects selection in the body of a conditioned pulp by causing gas bubbles to precipitate from solution in the liquid phase preferentially at the surfaces of collector-coated particles, and to cling to these particles, Gaudin2 states that, within the pulp body of an agitation machine, attachment of mineral particles to air bubbles occurs as a consequence of contact between the two. This theory has been supported by theoretical reasoning and much circumstantial evidence. Perhaps the most interesting bit of evidence in favor Of this theory js the difficulty in the flotation of fines. If attach-

Jan 1, 1949

By William G. Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the nonhomogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of deforming beyond the limit of purely elastic strains, a plasticity theory is required. The purpose of this chapter is to present a plasticity theory for anisotropic rocks and soils. The proposed theory is based on the work of Hill in anisotropic metal plasticity and represents an extension of his work so as to include anisotropic geologic materials. The point of departure from metal plasticity theory begins with the inclusion of the normal stresses as linear terms in the yield condition, which plays a central role in plasticity. Once the yield condition is established, the plastic strain increments are obtained immediately through the principle of normality. For practical applications, some simplification of the three-dimensional theory is re-

Jan 1, 1972