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By E. Gilpin

Any estimate of the economic mineral value of an unvisited district is to the mining engineer largely a comparative one. If he knows that certain minerals characterize any given geological horizon he naturally draws upon his experience of the same ores as met by him cinder similar geological conditions. And if he has not had the personal experience, the investigation of the geology of a similar district as given in a trustworthy report enables him to lay a fair basis for conclusions. In a general way these conclusions are of value, and while they pronounce on the possible mineral fecundity of a given district, they

Jan 1, 1890

By David L. Pentz

ABSTRACT A critical summary is given of the analytical procedures available to the engineer for the analysis of slope stability. The emphasis is on the various types of behaviour that have been measured in different rock types. A method of assessing the possibility of failure of simple three dimensional wedges is provided in an attempt to demonstrate how structural features can be included in a meaningful manner. An outline for theoretical design is provided that stresses the importance of carrying out a 'Back Analysis' of large and small instrumented failures so that realistic parameters of the rock mass forming the pit slopes can be obtained.

Jan 1, 1971

By J. A. Jargon, H. K. van Poollen

Flow of slightly compressible fluids through porous media can be described by linear equations. Many mathematical solutions- are available for the boundary conditions of constant terminal pressures or constant flow rates, or a combination of both. Various techniques of formation evaluation use drastic rate changes, such as sudden shut-in. Other methods require that the well be produced at a constant rate. In practice, one is not always able m fulfill these rigid requtirements. This report shows a methor1 by which varying-rate data can be converted to a constant-rate pressure response, called the unit response function. After obtaining the unit response function, one may analyze it, using techniques described in the literature. The method uses tile principle of superposition. Necessary data is a time history of pressure and production. If pressure changes and/or rate changes are very drastic, the unit response function becomes erratic and oscillates The erratic and oscillating results are obvious, and under those circumstances, no answer can he obtained. It appears, however, that a response function without oscilla-tion will not contain any appreciable errors —- one gets either good results or no results. This report includes a mumber of examples of converting constant-rate data to constant terminal-pressure data and vice versa. In addition, a number of field-test applications are given. This method should be useful in converting mathematical solutions from one boundary condition to another. It already has proven useful in converting varying-rate data to constant-rate conditions. INTRODUCTION Pressure drawdown tests are performed on production wells to determine various reservoir characteristics, including permeability, distances to discontinuities, reservoir continuity and wellbore conditions. An ideal drawdown test is performed at a constant production rate with pressure observation during the drawdown period. A typical drawdown curve for a constant rate of production is shown in Fig. 1. In practice, a constant production rate cannot always be maintained. Fig. 2 shows a pressure drawdown curve for a varying rate. Usual methods of analysis are not applicable to tests such as this. It is, therefore, necessary to convert the varying-rate data somehow, before usual analytical techniques can be applied. This report describes a method of obtaining a response function. A response function can be defined as the relationship between pressure and time for a well producing at a constant unit rate. Such a response function can be analyzed by the usual analytical techniques. Hutchinson and Sikora' first approximated a resistance function (response function), and by applying the superposition principle, pressures were calculated using the varying rates. If no match was obtained, adjustments were made to the response function and the closer approximation was used again in an attempt to match calculated and observed pressure behavior. If a good match was obtained: the response function was then used to extrapolate the future aquifer behavior.

Jan 1, 1966

Impact Transition Temperatures of Some Pearlite-Free Mild Steels As Affected by Heat Treatments in the Alpha Range H. P. Tardif (Canadian Armament Research and Development Establishment, Quebec)—Mr. Josefsson is to be congratulated for his study of a most difficult subject and for the theories proposed to explain the re- sults. One point which, however, might not have received proper attention is that of the shape of the stress-strain curve at the yield point of quenched and furnace-cooled specimens and of specimens strain aged

Jan 1, 1956

By N. O. Johnson, R. A. Westin

Polychlorinated biphenyls were the basis of non-flammable askarel dielectric liquids wed in electrical equipment made between 1929 and 1978. Although PCBs were widely used in mine electrical equipment, the toxicity and environmental persistence of this chemical led Congress to ban its manufacture and use. Bureau of Mines Information Circular 8838 summarizes the regulations imposed by the EPA on the use and disposal of PCBs, and describes the limitations of available substitutes. Recent changes in the regulations will impose additional requirements on the use of PCBs by the mining industry. This paper is an update of the material presented in the Bureau of Mines information circular.

Jan 1, 1983

By S. S. Hsieh, J. R. Lehr

Bench scale beneficiation studies were made on Idaho dolomitic phosphate rock using the TVA carbonate flotation process. The process used diphosphonic acid as a phosphate mineral depressant and fatty acid as a carbonate mineral collector. Silica was subsequently rejected as float using an amine collector, with phosphate product recovered as the sink fraction. Two samples of prepared flotation feed from commercial operation were used. One contained 21% P205 and 3.2% MgO. The other contained 26% P205 and 1.8% MgO. The results indicate that concentrates containing 31% to 33% P205 and 1% or less MgO can be obtained, with about 80% P205 recovery.

Jan 1, 1986

By Chester R. McKee, Robert W. Terhune, Merle E. Hanson

The relationships describing the enhancement of permeability by firing explosives in boreholes have been derived and combined to yield permeability enhancement as, [ ] or the case in which the stress decays asymptotically as a power law kc and nc represent permeability and fracture density at the edge of the pulverized region near the cavity wall, f is a geometric attenuation factor, m is the dissipation due to real material effects, ko is the original permeability and rd is the scaled radius. This relationship has been compared with available measurements from the American nuclear shot "Hardhat", the French nuclear events in Hoggar granite and the chemical explosive shot in coal near Kemmerer, Wyoming. Significant correlation between this theory and the experimental measurement is observed. A comparison between single and multiple detonations shows that permeability enhancement falls off steeply near the shot; however enhancement can be considerable midway between two shots spaced 10 cavity radii apart. The degree to which enhancement, can be significant depends on material properties and fracture density. Porosity distribution from the explosive 1s the dominate parameter in permeability enhancement. Existing theories of permeability enhancement have also been reviewed.

Jan 1, 1976

By R. R. Morral, F. M. Krill, K. T. Aust

THE occurrence of twins in aluminum ingots cast under certain conditions has been well established. For instance, Herenguel and Lacombe1,2 have observed a twinned columnar structure in 99.5 and 99.9 pct Al, solidified by continuous or semicontinuous casting. The structure, which they termed "basaltic," appears in the form of elongated crystalline fibers of alternating luster. Herenguel and Lacombe2 found sections of flat crystalline plates composed of twin crystal plates, in which the twin plane (111) and a [I121 direction contained in the twin plane are parallel to the principal heat gradient. This orientation relationship is different from the usual orientation texture observed in cast face-centered cubic metals, where the [100] direction is approximately parallel to the long columnar axes lying in the direction of growth." A large amount of twinning has also been observed by the present authors in semicontinuous cast aluminum of 99.2 pct purity, Fig. 1. Mondolfo4 has suggested that the twinned cast structure forms by a deformation twinning process as the result of uneven cooling stresses within the ingots. This suggestion appears to be inconsistent with the large amount of twinning observed in the semicontinuous cast ingots and with the large difference of dendritic

Jan 1, 1953

By J. W. Spretnak, V. Kandarpa, G. W. Powell, R. A. Erickson

Neutron-diffraction pattens were obtained at room temperature from two austenitic manganese steels, oxc wth n carbon content of 1.23 zct PC/ and the olher 0.63 wt pct. Analysis of the data showed that the curOan atols (ions) occupy tile octaheadral site. any of the cavbon is in the tetahedral site, tile concentration is too strzall lo be detecled by tzeulr-on d$facton. AS part of a long-range investigation of eutectoid decomposition, a study of the structure of austenite has been undertaken in order to characterize as best as possible the parent phase in the Fe-C system. Austenite is a solid solution of carbon atoms in fcc iron, the carbon atoms being located in interstitial positions. Of the two kinds of interstitial sites, octahedral (0, +, +) and tetrahedral (4, a, $), in this lattice, the larger octahedral sites are usually considered as the probable position of carbon. The strain energy involved in pytting a neutral carbon atom (covalent di; ameter 1.54)' into a tetrahedral site (diameter 0.56A) is considerably greater than that associated with p2tting carbon into the octahedral site (diameter 1.08A). Dayal and arkeen' observed the migration of carbon in iron under the influence of an electric field indicating tha tye carbon is ionized. pe ionic radius of C'4 is 0.15A and that of C" is 0.29. Consequently, it is conceivable that carbon ions could occupy the tetrahedral sites if one considers only the strain energy. Size considerations alone do not provide a complete explanation for the formation of the interstitial solid solutions, however. because metals such as copper, zinc, and cadmium do not appear to form interstitial solid solutions in spite of their large interstitial sites. Evidence which suggests partial ioni-zation of the carbon in austenite has also been obtained by Speiser, Spretnak, and alor who derived formu- lae relating the observed change in lattice parameter to the effective diameter of the solute atom. Assuming the carbon occupies the octahedral site. they computed the effective diameter of carbon to be 1.33A whereas the covalent diameter is 1.54A. petch5 concluded from powder X-ray diffraction experiments that carbon atoms occupy the octahedral sites. His conclusion was based on the general trend observed in the intensity of the diffraction lines as the carbon content of the austenite was increased. However, the major difficulty associated with application of X-ray diffraction to this particular problem is the relatively poor scattering power of carbon. Williamson and smallman' utilized X-ray diffraction to study the line broadening caused by the strain field about carbon atoms inferrite: these investigators concluded that at least 85 pct of the carbon in ferrite occupies the octahedral (0: 3, B) site rather than the larger

Jan 1, 1967

By G. F. Loughlin

MORE than 20 years have passed since the publication of Lindgren and Ransome's report on the Cripple Creek District,1 which was made when the district was much more active and prosperous than in recent years. They concluded that the output of the district, which had reached its maximum of about $18,200,000 in 1900, would gradually decline, and their conclusion has been confirmed by records of subsequent production. Between 1905 and 1915 annual declines were partly compensated by encouraging increases, especially in 1908, 1914, and 1915; but a rapid continuous decline followed, due largely to the war and its after effects, until in 1922 the value of output was only slightly more than $4,000,000. It rose to nearly $5,000,000 in 1924, but declined again in 1925 and in 1926, when it was about $4,400,000, and represented ores mainly from deep levels in the Cresson and Portland mines. The profitable operations of these two mines were the principal factors leading to a study of ore at deep levels in the district by the U. S. Geological Survey in coopera-tion with the Colorado Metal Mining Fund. The principal reasons for Lindgren and Ransome's conclusion were three: (1) the greater cost and difficulty of deep exploration; (2) the decrease in the number of veins with increasing depth, and (3) the probability that the telluride ore, believed to have formed at comparatively low temperature, would not persist indefinitely -in depth. Operations since they made these statements have verified the first two, but call for some modification of the third. Rich telluride, ore is being mined at a profit in the Portland mine 3000 ft. below the present surface, or 5000 ft. below the original surface of the Cripple Creek volcano, as interpreted by Lindgren and Ransome. The question arises, therefore, as to the number and extent of such deep deposits, and the answer, so far as it can now be given, must be based mainly on structural data, supplemented by data on the processes of ore deposition. Presentation of these data based on a study of deep mines in the southeast quarter of the district, the only

Jan 1, 1927

By Clarence Linville

IN an article published in the Iron. Trade Review 1 I gave a convenient arrangement for the installation of wet and dry bulb thermometers for use in making moisture determinations in the air being blown into a blast furnace, and also gave a chart for use in obtaining moisture values from the thermometer readings. The data from which this chart was prepared were obtained from the tables in use by the U. S. Weather Bureau.2 The work of Carrier 3 has shown that these tables are somewhat in error. He has recalculated the values for moisture as referred to, wet and dry bulb thermometer readings, and he has prepared a psychrometric chart from the values thus obtained. This work has priced the subject of psychrometry upon a correct scientific basis. I think it is proper that we should recognize the importance of his work and give him credit for one of the most interesting and valuable researches that have been published in recent years. Blast-furnace men are not ready to use, as he suggests 4 a value expressed in grains of water accompanying a pound of dry air. However convenient this may be for heating and ventilating work and other engineering problems, there are several reasons for preferring the use of a value expressed in grains of water in a. cubic foot of mixed air and water vapor, in connection with combustion phenomena and the effects of moisture on blast-furnace operation. Previous papers presented to the Institute have used such values and we have

Jan 10, 1913

By Clarence P. Linville

In an article published in the Iron Trade Review,' I gave a convenient arrangement for the installation of wet and dry bulb thermometers for use in making moisture determinations in the air being blown into a blast furnace, and also gave a chart for use in obtaining moisture values from the thermometer readings. The data from which this chart was prepared were obtained from the tables in use by the U. S. Weather Bureau.2 The work of Carrier3 has shown that these tables are somewhat in error. He has recalculated the values for moisture as referred to wet and dry bulb thermometer readings, and he has prepared a psychrometric chart from the values thus obtained. This work has placed the subject of psychrometry upon a correct scientific basis. I think it is proper that we should recognize the importance of his work and give him credit for one of the most interesting and valuable researches that have been published in recent years. Blast-furnace men are not ready to use, as he suggests14 a value expressed in grains of water accompanying a pound of dry air. However convenient this may be for heating and ventilating work and other engineering problems, there are several reasons for preferring the use of a value expressed in grains of water in a cubic foot of mixed air and water vapor, in connection with combustion phenomena and the effects of moisture on blast-furnace operation. Previous papers presented to the Institute have used such values and we have

Jan 1, 1914

By C. D. Wiseman

THE concept of alloying to increase the strength of metals originated during the bronze age. However, at the present time there is no single theory capable of explaining all of the observed strengthening effects of alloying elements on the mechanical properties. In general, it may be said that solid solutions are stronger than the pure metal and that the strengthening effect increases with increasing alloy content. Various theories for solution hardening have been proposed, the first of which was presented by Rosenhain who suggested that the alloying elements roughened the slip planes, thereby requiring a higher stress to initiate slip. Recent work by French and Hibbard2 confirmed Norbury's3 conclusion that those alloying elements which cause a greater change in lattice parameter have larger effects on hardness. However, a given change in lattice parameter produced by different alloying elements does not cause the same change in hardness. A further refinement was suggested by Dorn, Pietrokowski, and Tietz4 who considered differences in valence between the solute and solvent with the change in lattice parameter to explain the plastic properties of aluminum alloys. Allen, Schofield, and Tate5 further investigated the valency contribution to solution strengthening by testing some copper-base solid-solution alloys having constant electron densities. Tensile tests performed on these alloys gave identical stress-strain curves even though the atomic size effect, which varied by a factor of two, was neglected. The advent of dislocation theory6-8 provided a new and powerful tool capable of explaining many phenomena of plastic deformation and indicated new approaches to solution hardening. The basic con- cept of recent theories is that solution hardening is not due to stresses associated with randomly dispersed solute atoms, but rather to a nonuniform distribution of the solute. This conclusion was reached by consideration of the effective tension present on each dislocation line and the ability of a dislocation to pass an obstacle. cottrell suggested the possibility that the internal stresses due to randomly distributed solute atoms would offer essentially no resistance to the passage of dislocations. He reasoned that an edge dislocation may be considered as a rigid line discontinuity. As the dislocation moved through a crystal, the random stress fields would be equally distributed along its length. Since half of the stress fields would be acting to move the dislocation forward and the other half trying to move it back, the net effect on the dislocation would be zero. Thus the randomly distributed solute atoms would not contribute appreciably to solution strengthening. Mott and Nabarro10 considered the dislocation as a flexible, rather than a rigid, discontinuity. They obtained a simple model for a dislocation moving in a lattice having precipated particles, where the dislocation would actually bend around the obstacle until it would loop back onto itself to rejoin and then continue onward. Their work indicated that the minimum radius of curvature of the dislocation line, under the action of an external stress and in the region of an internal stress, would be such that the dislocation would be unable to pass through a matrix containing small closely spaced precipates by the looping process. The dislocations would tend to remain rather straight, approaching the condition of Cottrell's rigid dislocation. Hence, the strengthening must not be due to random solute atoms; however, it might be due to the concentration of atoms, either as clusters of like atoms or as short-range ordered regions, or to the concentration of solute atoms around dislocations. To date, four mechanisms of solution strength-

Jan 1, 1959

JAMES DOUGLAS Dr. James Douglas, twice President of the American Institute of Mining Engineers, and one of its principal benefactors, died in New York on June 25, 1918, at the age of 81 years. After a life of extraordinary activity, failure of his health compelled him to retire about 2 or 3 years ago, and in view of his advanced years his death was not unexpected. His funeral was held at the Church of the Mediator, on June 26, and was attended by representatives of the American Institute of Mining Engineers and of the Canadian Mining Institute. His body was then taken to Quebec for burial in the family plot. An extended notice of Dr. Douglas, prepared by Dr. R. W. Raymond, will be presented in the September issue of the Bulletin. LEWIS NEWTON BAILEY Lewis Newton Bailey died of pneumonia at Camp Merritt, N. J., April 30, 1918, at. the age of 34 years. He was Master Engineer, .Senior Grade, in the Fourth Regiment, U. S. Engineers; and although he was offered a commission as First Lieutenant shortly after enlisting, he preferred not to accept it until he had reached France. By those who knew him well, this lack of eagerness for promotion will be recognized as consistent with his whole character.

Jan 8, 1918

By Russell W. Dayton

THE metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concerning the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory - is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chalcography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Königsberger, (1)‡ in 1909, was the first to apply polarized light to the microscopic study of

Jan 1, 1935

By Russell Dayton

THE metallurgical polarization microscope has been utilized in several researches in the last few years, thus attaining a fair degree of prominence, but little has been written in a manner suitable to a metallurgist concern-ing the theory of this instrument. In this investigation the theory was carefully studied, and the results are presented here in a detailed manner, yet as simply as possible. The theory is discussed with particular reference to the three chief functions of the instrument: (1) determination of anisotropy; (2) effect of strain; and (3) identification of inclusions. Each of these is investigated experimentally, with especial attention to the mechanism of producing any effect. Where possible, the discussion is supplemented by photomicrographs. The instrument used had numerous defects as a polarization microscope; these and their remedies are discussed. In the microscopic study of transparent mineral sections (chal-cography) the use of polarized light has aided tremendously in the identification of a mineral. The determination of strain in transparent substances (photoelasticity) by the use of polarized light has lately become a commercial process, used in testing finished glass articles. The success of the use of polarized light with opaque materials has not been so great. The magnitude of the effects obtained is much less than that of the corresponding effects with transparent materials, and the mechanical difficulties are much greater. Konigsberger,(1)? in 1909, was the first to apply polarized light to the microscopic study of

Jan 1, 1935

By Walter S. McKee

Discussion of the paper of WALTER S. McKEE, presented at the New York meeting, February, 1916, and printed in Bulletin No. 108, December, 1915, pp. 2399 to 2411. J. W. RICHARDS, So. Bethlehem, Pa.-I regret that the author has overlooked the great usefulness of the electric furnace for the melting of ferromanganese in the manufacture of manganese steel. WALTER S. MCKEE, Chicago, Ill. (communication to the Secretary*)-In an article as brief as mine it was not possible to .fully cover the metallurgical field; this accounts for my not mentioning the electric furnace for the melting of ferromanganese in the manufacture of manganese steel, although the advantages of such an apparatus are fully appreciated by me. FREDERICK LAIST, + Anaconda, Mont. (communication to the Sec-retary?).-Manganese steel has proved very serviceable in our plant.. We are using manganese steel for the jaw plates on the 5-' by 15-in. crushers in the concentrator instead of cast-iron jaw plates which we formerly used. The manganese steel wears five times as long as the cast iron. We are also using manganese steel in our 8- by 20-in. crushers. In our primary crushers, which are 12 by 24 in., we still use cast iron because the manganese-steel plates wore unevenly and left shoulders which caused trouble in setting up the crusher. Another reason for preferring cast iron in these crushers is that they grip the ore better on account of wearing of the rougher surface. The surface of the manganese steel becomes polished and large pieces of ore fail to be drawn in. We recently tested 8- by 16-in. manganese-steel elevator buckets working on 2-in. undersize against malleable-iron buckets and found that manganese-steel buckets lasted two and one-half times as long as the malleable-iron buckets. We use manganese-steel screen plates on our 2-in. trommels and have found that they last about five times as long as cast iron. We also used manganese-steel wheels and rails under the 20-deck round table in our slimes-treatment plant. We first used cast-iron rails and wheels and found that these wore badly at the end of two or three weeks, while the life of the manganese steel seemed to be almost indefinite; we never had occasion to change any of the manganese steel rail sections or wheels in the year and nine months that the plant was in operation.

Jan 5, 1916

By L. M. Johnson, C. G. Janes

INTRODUCTION In May, 1966, the General Services Administration (GSA) announced a program to encourage additional domestic production of copper in the interest of national security. Upon learning of the copper production expansion program, Duval Corporation entered into negotiations with GSA for development of the Sierrita copper-molybdenum property under the program. Agreements between the GSA and Duval Sierrita Corporation, a wholly owned subsidiary of Duval Corporation, were concluded in 1967, with the Sierrita Concentrator beginning operation in 1970 at a designed capacity of 72,000 STPD. Subsequent additions and modifications have expanded capacity to 90,000 STPD. This property, located approximately 20 miles south of Tucson, Arizona, represents an investment including working capital of about $200 million. These funds were provided from an $83 million loan from GSA, repayable in copper valued at 38 cents per pound, $48.75 million of bank loans subject to U. S. Government V-loan guarantees, and Company capital contributions. Current general operating statistics for the concentrator are listed below: [Ore Grade 0.32% Cu., 0.030"/. Mo. Daily Tons Milled 90,000 STPD Annual Copper Product ion 94,600 Tons Annual Molybdenum Production 15,000,000 Lbs. Annual Silver Production 1,135,000 Ounces]

Jan 1, 1976

By R. W. Gurry

IN the course of a series of measurements of the rate of diffusion of carbon in austenite at about 960°C. (1760°F.) and 1110°C. (2030°F.), it became necessary to determine carbon concentration when austenite is saturated with graphite, because of indications that the hitherto accepted value of the solubility of graphite in this temperature range is too low. Specimens of carbonyl iron were saturated at temperature in a hydrogen-toluene atmosphere which was in equilibrium with graphite. The carbon content of the steel was measured either by combustion or by the loss of weight after substantially complete decarburization in an atmosphere of hydrogen saturated at room temperature with water vapor. The absence of carbide or graphite as a phase at temperature was demonstrated by microscopic examination of saturated specimens that had been drastically quenched. The mean result of concordant measurements is that gamma iron saturated with respect to graphite contains 1.39 per cent carbon at 957°C. (1755°F.) and 1.89 per cent at 1110°C. (2030°F.). These two values, plotted along with what appears from the literature to be the best value (0.69 per cent) at the iron-graphite eutectoid temperature (738°C. or 1360°F.), yield a curve that is almost linear, and which, continued upward through a short interval, leads to a limiting solubility of 1.98 per cent at the iron-graphite eutectic temperature 1135°C. (2075°F.) instead of the commonly accepted value of about 1.7 per cent. EXPERIMENTAL PROCEDURE The samples of carbonyl iron, with the exception of those for microscopic examination, were cylinders 3.8 cm. long, 0.475 cm. in diameter. They were placed in a graphite holder and suspended in a vertical furnace, the temperature of which was controlled precisely by means of the resistance of the platinum winding.1 In the empty furnace the range of temperature over a distance of 4 cm. at the heat center was 9°C. (16°F.) but at a given location the temperature remained within ±0.5°C. (0.9°F.); it was measured by inserting a platinum-rhodium couple calibrated at the melting point of palladium, 1555°C. Since the presence of the sample probably improved the uniformity of temperature, it was decided to consider the average temperature of the sample to be 3°C. lower than the maximum measured in the empty furnace with the same setting of the controller. Data were obtained in the vicinity of two temperatures, 960°C. (1760°F.) and 1110°C. (2030°F.). The samples for microscopic examination, 2.2 cm. long, 0.475 cm. in diameter, were suspended individually on pure iron wire; for these no temperature correction was applied. The carburizing gas passed into the furnace was dry, oxygen-free hydrogen saturated at room temperature with

Jan 1, 1942

By G. Rowan, M. W. Clegg

The basic equations for the flow of gases, compressible liquids and incompressible liquids are derived and the full implications of linearising then discussed. Approximate solutions of these equations are obtained by introducing the concept of a disturbed zone around the well, which expands outwards into the reservoir as fluid is produced. Many important and well-established results are deduced in terms of simple functions rather than the infinite series, or numerical solutions normally associated with these problems. The wide range of application of this approach to transient radial flow problems is illustrated with many examples including: gravity drainage of depletion-type reservoirs; multiple well systems; well interference. INTRODUCTION A large number of problems concerning the flow of fluids in oil reservoirs have been solved by both analytical and numerical methods but in almost all cases these solutions have some disadvantages — the analytical ones usually involve rather complex functions (infinite series or infinite integrals) which are difficult to handle, and the numerical ones tend to mask the physical principles underlying the problem. It would seem appropriate, therefore, to try to find approximate analytical solutions to these problems without introducing any further appreciable errors, so that the physical nature of the problem is retained and solutions of comparable accuracy are obtained. One class of problems will be considered in this paper, namely, transient radial flow problems, and it will be shown that approximate analytical solutions of the equations governing radial flow can be obtained, and that these solutions yield comparable results to those calculated numerically and those obtained from "exact" solutions. It will also be shown that the restrictions imposed upon the dependent variable (pressure) are just those which have to be assumed in deriving the usual diffusion-type equations. The method was originally suggested by Guseinov,1 who (a) postulated a disturbed zone in the reservoir, the radius of which increases with time, and (b) replaced the time derivatives in the basic differential equation by its mean value in the disturbed zone. In this paper it is proposed to review the basic theory leading to the equations governing the flow of homogeneous fluids in porous media and to consider the full implications of the approximation introduced in linearising them. The Guseinov-type approximation will then be applied to these equations and the solutions for the flow of compressible and incompressible fluids, and gases in bounded and infinite reservoirs obtained. As an example of the application of this type of approximation, solutions to such problems as production from stratified reservoirs, radial permeability discontinuities; multiple-well systems, and well interference will be given. These solutions agree with many other published results, and in some cases they may be extended to more complex problems without the computational difficulties experienced by other authors. THEORY In order to review the basic theory from a fairly general standpoint it is proposed to limit the idealising assumptions to the minimum necessary for analytical convenience. The assumptions to be made are the following: 1. That the flow is irrotational. 2. That the formation is of constant thickness. 3. Darcy's Law is valid. 4. The formation is saturated with a single homogeneous fluid.