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By Potts N. L., Eilerts C. K., Summer E. F.

The second-order, nonlinear, partial- dillerential equation representing the transient radial flow of gas - condensate fluids in reservoirs has been integmted by using finite -dillerence equations and electronic computers. Effect was given to pressure -dependent permeability, viscosity, and compressibility and to distance-dependent permeability. The influence of a second-degree velocity term in the Darcy equation was investigated. Implicit methods were used and practical, convergent solutions were obtained with material balance to less than 6 x 10-4 for recovery of one- hall the reserve at constant flow rate. Integration results provide the productive period of a reservoir for a given constant rate and the fraction of the fluid initially in place that can be recovered in that period. The properties of a lean and a rich fluid are represented in a set of integrations designed to demonstrate the effect of different constant-recovery rates and significant variables emphasized one at a time. INTRODUCTION A method is needed for computing the availability or reserve of a gas in a formation, making use of all technical and engineering information that is pertinent. As a step in this direction, a program for computing transient linear flow1 was developed that utilizes principles of earlier finite-difference computing for a similar purpose2-4 and gives effect to significant pressure- and distance-dependent properties of reservoirs and their contents. The present paper pertains to transient, radial flow of gas-condensate fluids. In the partial-differential equation of flow, effect is given to the variables viscosity and compressibility,5 and also to permeability. Included in the study is the quadratic form of the Darcy equation of flow that has been the subject of field tests6 and that has been applied to a gas with constant properties in transient flow computing. 7 Inclusion in the differential equation of variable coefficients to represent properties greatly complicates the higher derivatives of the equation. Because it was impractical to make a required improvement in certain of the finite-difference derivatives by Taylor-series expansion, five-term derivatives were used in the implicit computing. Related methods were developed that can improve general facility in manipulating finite-difference equations. BASIC EQUATIONS PARTIAL DIFFERENTIAL EQUATION The basic partial differential equation for transient radial flow in the direction of decreasing radius is l_ a(vpr) _? .......(1) r gr at where r = radius, L v = apparent velocity aIong radius, L/t p = density, M/L3 t = time, t Ø = porosity, dimensionless. In this equation, only the porosity is regarded constant. The density is where p = pressure, m/Lt2 M = molecular weight of fluid, m T = constant temperature of fluid, T z(p) = pressure-dependent compressibility factor, dimensionless R = gas Constant, mL2/t2t. The physical boundary of the reservoir is at re, and the producing boundary is defined to be at tq with rq = re /200. By definition,

Jan 1, 1966

F A. THOMSON, president of the Montana School of Mines, gave an interesting talk on mining schools of the past, present and his ideas of the future before a recent meeting of the Montana Section of the A. I. M. E. He covered the history .of the various mining schools and com- pared the three main types of schools; those attached to or forming part of an endowed college or university such, for example, as' the Columbia School of Mines, the Mining Department of the Massachusetts Institute of Technology and the Mining Department of Stanford University. These resemble in a general way the second class, those attached to the state universities and colleges. The schools of this general type have had varied success.

Jan 1, 1928

By H. K. Birnbaum

The termination of a twin lamella in the interior of a crystal requires accommodation of the strains at the tip of the twin which result from coherency of the twin and matrix. In zinc and magnesium crystals,

Jan 1, 1960

By M. Guney, A. R. Bell

In Mindola mine on the Zambian Copperbelt, there is a plan to extend the current production level of 1.2- 1.5 km (3,900-4,900 ft) with five additional production levels. Research work indicated that the present total heat output of 38.6 MW will inevitably increase to 63.2 MW in 25 years. Estimated WE and DB temperatures, representing the total heat generation in stope faces and development headings during these same periods are predicted to increase to 33.8/40.2°C (93/104°F) and 35.3/42.1°C (95/108°F) respectively. It is assessed that the nominal refrigeration capacity needs to be progressively increased to 9,000 M W.

Jan 1, 1984

By J. P. Nielsen

When two grains in a polycrystalline specimen meet at a point in the course of grain-boundary movements, and the new boundary created at the point is one of relatively low specific free energy, a nonequilibrium boundary condition occurs. The nonequilibrium is enhanced if the other grain boundaries involved at the point of meeting are relatively high in specific free energy. The nonequilibrium results in a correction by growth of the complex grain (two subgrains) to a large size, sufficient in many cases for it to become a self-propagating unit, i.e., a recrystallization grain. This mechanism, herein called "geometrical coalescence," is proposed as a logical origin for recrystallization nuclei, particularly for secondary recrystallization. RECENT publications1-' indicate that considerable progress has been made toward a complete understanding of the three microstructural processes in metals: recovery, recrystallization, and grain growth. However, a major problem persists, namely, the origin of recrystallization nuclei. It is generally accepted that once a recrystallization nucleus, a secondary recrystallization nucleus particularly, has reached a certain size, it will continue to grow at the expense of its neighbors, simply as a consequence of grain-boundary free-energy considerations. What has remained obscure, however, is the mechanism whereby such a nucleus comes into being and grows to the self-propagating size. Recrystallization Nucleation in a Two-Dimensional Grain-Boundary System In the left portion of Fig. 1 is shown schematically the meeting of grains 1 and 4 on disappearance of boundary 2-3, i.e., the boundary that existed between grains 2 and 3, as might happen in the course of normal grain-boundary migration. If, by chance —and the probability is not necessarily small— grains 1 and 4 are close together in their mutual orientations, or in some other special way mutually oriented so that the new common boundary has relatively a very low specific free energy (hereinafter referred to by s), then the grain boundary arrangement as depicted in the figure is highly unstable. This is particularly so if boundaries 1-3, 3-4, 4-2, and 2-1 are high in their s values. Assuming, for the sake of argument, that boundary 1-4 has a s equal to zero, and the s's of all the other boundaries present are equal to each other and constant, then the boundary arrangement on the right in Fig. 1 will be

Jan 1, 1955

By Gerald Edmunds

In a paper1 before this Institute in 1940, the writer reported that the surface orientation texture of zinc and cadmium differed from the texture existing within the casting, in that basal planes were parallel to the surface. He was unable to rationalize the , origin of this surface texture. It is conceivable that the surface orientation texture is influenced by the atomic force fields, which are different at the surface and within the body of metal. It was considered that a radical changc in the surface against which the metal is cast might alter the surface texture. In trial of this, zinc has been cast against a surface of molten lead, but the same result has been obtained—i.e., (001) parallel, ± 2oo, to the surface—as was obtained when it was cast against air, Transite or iron.' Into the bottom of an open cast-iron tray, 7 by 14 in. by 2 in. deep, preheated to about 275°C., about 1/4 in. of lead, then 1/2 in. of zinc was poured, and the whole was covered with an electric heater to enforce freezing from the bottom upward. After a lapse of time sufficient for the zinc but not the lead to solidify, the zinc slab was raised free of the molten lead. The bottom surface of the zinc casting was coated with a thin layer of lead. A specimen of the slab 136 in. square was metallographically polished to flatten it and remove the slight film of lead, and the orientation was determined by the method used before,' with the result stated above. Some determinations have also been made on other metals, as follows: Surface orientation determinations were made on the 3/8-in. diameter grip section of two 1/4-in. diameter aluminum-alloy die-cast tensile bars and on a 1/8 by 1/2-in. flat aluminum-alloy die-cast tensile bar. None of these three aluminum die castings exhibited any preferred orientation at the surface. A brass die casting (nominal composition: 60 Cu, 37.75 Zn, 1.00 Sn, 1.00 Pb, 0.10 Al, 0.15 Si) furnished by C. S. Smith was also examined. The surface showed a random orientation of alpha and beta. Summary A zinc casting solidified against a molten lead surface was found to have the same surface orientation texture, (001) parallel to the surface, as other zinc and cadmium castings. Aluminum and alpha-beta brass die castings were found to have random grain orientation textures at the surface. Acknowledgment The X-ray determinations were conducted by M. L. Fuller.

Jan 1, 1945

By Dunbar D. Scott

The development in the perfection of mine-surveying instruments has been by no means rapid, as it has depended somewhat on the details of construction borrowed from astronomical and geodetic theodolites, largely on the restrictions laid down by mining companies and the prejudices of mine managers themselves, but more than all on the methods used in conducting surveys and the importance attached thereto. Mine-surveying, in some form or other, has been practiced from the very earliest times; but it has never kept pace with the other branches of surveying, or even with the art of mining itself, and cannot be recognized as an exact science until shortly before the beginning of this century. The works of Hero of Alexandria, who lived in the second century B.C., are still extant, and contain descriptions of a rectangular sighting-instrument, which he invented and called a diopter. His improvement upon this simple construction, which possibly he devised for use in the Greek mines for rough leveling-purposes and for laying out any angle, must be considered, says Hübner," as the origin of the highly perfected theodolite of to-day. Whether this instrument came into general use during the first centuries of the Christian era, is not recorded; in fact, no writer undertakes to tell how mine-surveying was conducted until 1556, in which year Agricola expounds the principles of mining and metallurgy in his De Re Metallica, devoting the entire fifth chapter to the practice of mine-surveying (see Fig. 1). In mediæval times those who possessed any knowledge of engineering skill made strenuous effort to keep their art a secret, partly on account of the miners' proverbial conservatism and partly for their own personal aggrandizement, and were, in

Jan 1, 1899

By NORMAN EBBLEY

NUMEROUS references have been made recently to "Alaska's oil reserves," and in view of the wartime petroleum situation sober thinking demands a dispassionate and scientific study and investigation of these reserves or supposed reserves. The question naturally arises, "Is there actually oil in Alaska, or are the reserves there a supposition?" True, in 1923 President Harding established Naval Petroleum Reserve No. 4 in Alaska, certainly implying that oil was there. This reserve, embracing about 35,000 sq. mi., was set aside on the advice of the Bureau of Engineering of the Navy Department and was based upon the existence of known petroleum seepages at Cape Simpson on the Arctic coast. The Cape Simpson seepages have been known for more than fifty years, but in spite of persistent rumors of other seepages in northern Alaska no definite evidence of their existence has been available.

Jan 1, 1944

By ROBERT R. ABUOTT

(Cleveland Meeting, October, 1912.) THE practice of carbonizing steel for the purpose of case-hardening has assumed great commercial importance within the past, 10 years. Formerly, case-hardened steel was held in more or less contempt, since it. was considered a cheap substitute for tool-steel. This is no longer the case. The development of the motor-car industry, and coincidentally that of modern alloy-steels, has resulted in overcoming many difficulties formerly experienced in case-hardening. This result has been accomplished by increased knowledge regarding the analysis of the steel which would respond most readily to case-hardening, and by more careful methods of treatment of the carbonized steel. The ordinary method of carbonizing consists in packing the steel with the carbonizing-material in cast-iron boxes and placing them in a furnace at a temperature of from 1,500° to 1,900° F. for a time sufficient to give the required depth of cc case." The steel is then either quenched directly from the box, or is allowed to cool without unpacking, and finally given a single hardening-heat., or, for special work, two or three heats. During the year 1911, more than 100,000 tons of carbonizing-material was sold in the United States, at an average price of probably $55 per ton. More than 85 per cent. of this material consisted of granulated bone. Within the past four years, many manufactured compounds have been placed on the market, consisting largely of some form of carbon or carbonaceous material, with or without the addition of chemicals. Steel will absorb carbon placed in contact with it at the temperature of the atmosphere. The reaction is exceedingly slow, but. increases rapidly with increasing temperature. Below * Metallurgical Engineer, The Peerless Motor Car Co.

Dec 1, 1912

By John W. King, S. Ralph Austin

Spurred by recent forecasts of greatly increased demands for uranium by 1980 and beyond, interest is once again focusing on America's western uranium deposits. One of the principal producers in this area is the Gas Hills district in Wyoming, the site of approximately 12% of the known uranium in the U.S., including past production and current reserves. Located on the south flank of the Wind River Basin, the Gas Hills deposits have been recently studied by the Atomic Energy commission for clues to and guides for discovering similar-occurring ores. The ore deposits are confined to a permeable sandstone unit, up to 350 ft thick, at or near the base of the upper Wind River formation of early Eocene age. The uranium occurs in three principal north- south "ore trends," each of which is about six miles long, one mile wide, and separated from each other by approximately three miles (Fig. 1).

Jan 5, 1966

By Russell B. Cornell, William B. Plank

AT the close of the academic year 1940-'41 the largest number of students ever recorded received their first or bachelor degree in the mineral technology schools of the United States. The total of men thus prepared to enter their professional careers in the mineral industries was 1601, a number nearly 12 per cent larger than two years ago and nearly 75 per cent larger than four years ago. Notwithstanding this increase in the number of graduates and as had been predicted in the preliminary report in February, there was a slight decrease in the total student population of the schools in both the United States and Canada. During the college year 1940-'41, 9133 students were enrolled in the 54 schools of the United States and 764 in six of the seven schools of Canada.

Jan 1, 1941

In the Philippines, where distances are spoken of in terms off fight time, the Sipalay copper mines are two flight hours southeast of Manila on the island of Negros. After landing at the airport in Bacolod, it is then 170 km (106 milers) by surface transportation to Marinduque Mining and Industrial Corp.'s expanding copper operation. While copper deposits were discovered in the area in 1936-and one mine, the Binulig, began operations soon after-it wasn't until 1956 that stripping at Sipalay and construction of a 4000-t/d (4400-stpd) mill began. The mill went into operation in May 1957, and the first shipment of copper concentrate was made three months later.

Jan 8, 1978

What is a conflict, as it is understood by men of the extractive industries? And what are the circumstances out of which these conflicts arise? A start can be made with the notion of economic conflict, which can be defined as rivalry over the use of economic resources. Such rivalry is a central part of all economizing activity. It is present within the individual, within the family, and within the business firm. In each of these units there are multiple goals competing for use of a limited income. And economic rivalry is present among individuals and firms who are competing with one another for use of the limited quantity of economic resources available to us as a society.

Jan 7, 1961

By Samuel Wyer

Over 8,000,000 people in the United States depend on natural gas for their cooking, heating and lighting service. This service has been made possible only by the investment of large amounts of capital in transportation lines connecting the gas wells to the various communities, thus combining a hazardous mining operation with a public utility service. The effect that making these lines " common carriers" will have on the present and future service to these 8,000,000 or more people is of far reaching ethical and economic importance, and deserves careful consideration. As an introduction, it must be conceded that: 1. Natural gas, although a mineral and obtained by a mining operation-with more uncontrollable and uncertain features to cope with than exist in the mining of coal or other minerals-when served to the public becomes a public utility service. 2. The governmental power to regulate all public utilities in the interests of the public cannot be successfully disputed. 3. Mere suggestion of inconvenience to the utility is wholly irrelevant, as it cannot be considered or allowed to influence in making a defense against governmental regulation. Unfortunately it is not generally appreciated that: 1. Legislative enactments are not necessarily laws, and cannot abrogate economic laws or alter engineering facts. 2. There is a clear distinction between "common carrier" and "public utility," although the terms are frequently confused. ' "A common carrier is one who undertakes for hire to transport persons or goods, or both, from place to place for all persons indifferently, the term implying indifference as to whom shall be served, and an equal readiness to serve all who apply, in the order of their application." On the other hand, property becomes a "public utility" only "when for a particular purpose the public have a right to resort to the premises and make use of them."

Jan 5, 1914

By A. E. Back, S. F. Ravitz

When manganese ores are leached with sulphur dioxide, a large part of any zinc in the ore usually is extracted with the manganese.1 In the dithionate process,2,3 in which the manganese ore is leached with dilute sulphur dioxide gas and the manganese is subsequently precipitated by adding lime to the pregnant solution, the zinc is precipitated with the manganese. These facts suggested the possibility of applying the dithionate process to the recovery of zinc from oxidized ores or calcined sulphide concentrates. Accordingly, an investigation was begun, and preliminary tests were made on several ores and concentrates. The results were encouraging, but the need to devote available funds and personnel to other projects made it necessary to drop the work before the various factors involved in the process could be studied in detail. A brief mention of the process,4 however, elicited a number of inquiries, so that it appeared desirable to report the results of the preliminary work. The dithionate process as applied to zinc may be summarized briefly as follows: The ore or calcined concentrate is leached with dilute SO2 gas to dissolve the zinc, largely as zinc sulphate, in accordance with the following equation in which [ZnO] represents the "oxide zinc" in the ore or calcine: [ZnO] + SO2(g) + 1/2 O2 = Zn++SO4— [1] If, in the leaching step, the ore or calcine is suspended in calcium dithionate solution, the sulphate ion, as it is formed, is precipitated immediately as calcium sulphate, which is subsequently filtered off with the insoluble ore residue: Zn++SO4— + Ca++S2O6— = CaSO4(s) + Zn++S2O6- [2] An alternative procedure is to suspend the ore in water, filter off the insoluble ore residue after leaching, add calcium dithionate to the resulting zinc sulphate solution, and then filter off the calcium sulphate precipitate. In either event the zinc is obtained in the form of a pregnant solution of zinc dithionate, from which it can be precipitated as relatively pure zinc hydroxide by adding milk of lime: Zn++S2O6— + Ca(OH), = Zn(OH)2(s) + Ca++S2O6- [3] The zinc hydroxide precipitate is calcined to form the final zinc oxide product: Zn(OH)2 = ZnO(s) + H2O(g) [4] Theoretically the process is completely cyclic with respect to dithionate ion, the calcium dithionate required for reaction 2 being replaced by that formed in reaction 3. In practice, of course, small amounts of dithionate would be lost in the various filter cakes, depending on the economic washing limits. In the leaching step, however, some of the SO2 is oxidized to dithionale instead of sulphate, accord- ing to the following overall reaction: ZnO + 2SO2(g) + 1/2 O2(g) = Zn++S2O6-, [5] so that the dithionate losses are made up, at least in part. Ores and Concentrates Tested The analyses of the ores and concentrates tested are summarized in Table 1, which also includes the analyses of the calcines produced from the concentrates. The concentrates were roasted in a laboratory muffle furnace at the temperatures indicated until evolution of SO2 could no longer be detected; shallow clay dishes ordinarily were used; but calcines 2a and 2c were prepared in iron dishes, with the result that these two calcines were badly contaminated with iron scale. The "complex" concentrate, sample 1, consisted essentially of sphalerite grains containing inclusions of pyrite and other sulphide minerals too minute to be liberated by grinding within economic limits. In the " marmatitic" concentrate, sample 2, the iron was present largely as marmatite (that is, as iron sulphide in solid solution in zinc sulphide) rather than as pyrite inclusions. The zinc was present largely as the carbonate in the two "oxidized" ores, samples 3 and 4, and as the silicate in the "willemite" ore, sample 5. Leaching Tests The leaching cell was a 3-liter glass beaker placed in an electrically heated water bath manually controlled to maintain a temperature of 35°C in the leach slurry. The slurry was agitated by means of a flat paddle-type stirrer

Jan 1, 1950

By Joseph A. Holmes

The public is already familiar with the general fact that the scope and the financial resources of the approaching St. Louis World's Fair are much larger than those of any of the preceding great expositions; and both the visitor and the exhibitor, when he comes to St. Louis in 1904, will find it to be a real World's Pair, with exhibits and visitors from every known country. Passing over the subject, as to the general Exposition, with this brief statement, I ask Sour attention to the consideration of a few important facts connected with the proposed mining exhibits at this Exposition. First of all, I may say that. reading- and writing-rooms and library facilities will be furnished in the Mines Building for miners and mining engineers, and it is expected that when they visit the Exposition they will make these rooms their headquarters, and give the Chief of the Department and his assistants an opportunity to extend to them such courtesies as may be possible. One of the exhibits in the Mines Department will consist of models and maps arranged to show the nature and extent of the mining operations in the United States at the time of the purchase of the Louisiana Territory in 1803, the event which

Jan 1, 1903

By JOHN A. FULTON

THE Comstock Lode is in Storey County, Nevada, and extends in a north and south direction through the towns of Virginia City and Gold Hill, with a total length of 4.27 miles. Its mines have produced silver and gold to a known value exceeding $400,- 000,000 since 1859, when the work first began. More than $126.000,000 was paid in dividends by the mining companies, although much more than this was probably realized from the ore, because many milling companies were independent companies owned by the directors and superintendents of the mines. The milling companies' contracts called for an extraction of only 65 per cent and, as much of the ore was worth $100 a ton and up- ward, they must have recovered substantial amounts for their own accounts over and above this guarantee. Gold was discovered in the spring of 1850 by a party of Normons bound for California. The discovery was made at the mouth of Gold canyon near Dayton, on the Carson River, about 10 miles south of Virginia City.

Jan 1, 1929

By N. L. Hancox

Previous researchers have used the cutting and rejoining model to represent a porous body when attempting to place Archie's law on a theoretical basis and calculate rock permeabilities (F = Ø-m, where F = formation factor, = - porosity and m = a constant). In using the model, a porous solid is assumed to consist of sections with parallel sides containing straight. continuous pores of total porosity 4 (pore to total volume or, for a homogeneous body, pore to total area). The joining of pores at an interface between two sections is assumed to be random which results in a common pore area Ø2. This reduced area Ø2 is then taken as that area which limits electrical conduction or fluid flow in the body. Agreement between experimental results and results calculated using a model is not always good Because of this, various modifications of the model are presented — for instance, the random nature of the joining is questioned. Formation factor measurements on specially constructed porous specimens are described in this paper. it is concluded that the common pore area limits flow completely only if sections containing straight pores are very thin, and that, in most natural materials, the common pore area at an interface must be greater than that given by random joining. However, the model is still useful in permeability calculations, provided that the fractional area limiting flow is determined from formation factor measurements. INTRODUCTION Two important properties of porous media are permeability k, which describes the ease with which a fluid can flow through a porous medium, and formation factor F, defined as the ratio of the resistivity of a saturated specimen to the resistivity of the saturating liquid which describes the electrical properties of the saturated material. k is defined by Darcy's law,l k= µqL/P Ae . . . . . . . . . . . . . . . [1] where µ = liquid viscosity, q = flow rate, L = length of specimen, p = pressure across the specimen and = - the effective area over which flow occurs, F is given experimentally by Archie's law,2 F = Ø-m ,..............(2) where 4 is porosity defined as the pore to total volume or, for a homogeneous body, the pore to total area; and m lies between 1.3 for loose sand and 2 for cemented sand. Consider a porous body of total cross-sectional area A and length L, saturated with a liquid of resistivity R and with an effective area for conduction of Ae. Then, from the definition of F given previously, F=A/Ae , ................(3) or, from Eqs. 2 and 3, Ae = A Øm ..............(4) Thus, in any attempt to calculate k or F, some assumptions must be made concerning the pore structure of the body and a value derived for A,. To determine Ae, Childs and George3 and Wyllie and Gardner4 suggested an elementary statistical representation often referred to as the cutting and rejoining model of a porous body. The body is assumed to be composed of two or more parallel-sided sections of porosity 4, containing straight, continuous pores with a common pore area of Ø2 at an interface between two sections. The value is given by a random joining of the pores in either section. Two such sections,

Jan 1, 1969

By C. M. Young

THE safety lamp is the most common and convenient apparatus for detecting inflammable gases in mines, the presence of gas being shown by a blue flame, called the cap, if the wick has been lowered to suppress the luminous flame. The height of the cap increases with the proportion of gas and with the temperature of the lamp flame. Lamps of the Wolf type, the fuel of which is benzine, have a hotter flame than lamps in which vegetable oils are used, such as the Davy, and the Clanny, and are more sensitive than the latter and their many modifications. The Piehler alcohol lamp gives a still higher cap while the Clowes hydrogen lamp is most sensitive of all. While the effect of the temperature of the source of ignition is well known, the writer knows of no previous attempt to correlate the change of this temperature with change of the height of the cap produced. In order to determine the height of the cap at various temperatures, it was necessary to have a source of ignition the temperature of which could he accurately controlled over a considerable range. This condition was met by a coil of wire of high fusing point heated by an electric current controlled by a variable resistance. The use of a coil offered the further advantage of freedom from complications due to the flame of a burning fuel. Such a flame, being itself of variable height, would to some extent raise or lower the elevation of the base of the cap and therefore add to the difficulty of determining the height of the cap. Besides this, the presence of a small cap from the lamp fuel, commonly known as the "fuel cap, " would interfere with the observation of small gas caps. After some experiment, a coil was made of platinum wire, No. 26, diameter 0.016 in. The coil was 17/64 in. (6.746 mm.) in outside diameter and had eight full turns in a length of ½ in. (12.69 mm.). This was connected to an electric circuit through an adjustable resistance, as shown in

Jan 8, 1919

In the Bowen Basin of central Queensland, coal production has gone from virtually nothing in 1961 to more than 24 million tons today4ut there's a cloud over this success.

Jan 1, 1977