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By W. J. West, W. W. Garvin, J. W. Sheldon

One of the most important problems of reservoir mechanics is the prediction of the behavior of a gas and oil producing reservoir for a variety of production programs. In the absence of a knowledge of the behavior of even idealized systems, it has been difficult, if not impossible, to determine which production program would yield maximum economic recovery. The problem was formulated mathematically many years ago, hilt a solution of the equations had never been obtained because of their extreme complexity. The solution of the problem became possible, however, with the advent of modern computing machines. This paper describes a digital method of solving the problem and discusses some of the results which have been obtained to date. The IBM Type 701 Electronic Data Processing Machines located at IBM's New York Scientific Computing Service were used successfully to perform the computations. The flow of gas and oil through a reservoir can be described mathematically by two second-order, nonlinear partial differential equations which must be solved simultaneously. All derivatives were replaced by finite differences to bring the equations into a form suitable for digital calculations. A number of finite ditference formulations were investigated and one form was found which resulted in stable, convergent solutions. This form was used to obtain .solutions for both radial and linear systems producing by solution gas drive. The results presented in this paper are: (a) saturation profile within the hypothetical reservoir vs. time, (b) pres.strre profile within the hypothetical reservoir vs. time. (c) gas-oil ratio vs. cumulative recovery, and (d) ultimate recovery. The saturation profile clearly shows the effect of critical gas saturation. The saturation near the well-bore drops quickly to the critical gas saturation and remains essentially at that value until the remainder of the reservoir also has dropped to the critical gas saturation. The pressure profile shows a smooth variation of pressure across the reservoir. The gas-oil ratio drops slightly during the early stage of production until the critical gas saturation is reached, rises rapidly from then on and eventually passes through a sharp maximum just before the economic limit of production is reached. For the radial example presented in this paper, the average oil .saturation of the reservoir at a time corresponding to the limit of economic production was 56.5 per cent and the ultimate recovery was 6.86 per cent. The difference between change in saturation and ultimate recovery is caused by .shrinkage of the oil phase. The solution time with the 701 Computer is sufficiently short to permit an economically feasible investigation of the effects of variation of the many parameters which describe an oil reservoir. In particular, the ultimate recovery for various systems can he determined as a function of rock and fluid properties, of well spacing. and of production rate. INTRODUCTION The effective planning for maximum economic depletion of oil reservoirs is one of the major problems confronting oil producers. The most important part of the planning is prediction of the response of the oil reservoir to a particular production program. The production program can be selected by imposing certain controls available to the operator. Some of these controls are: (a) well spacing, (b) production rate, (c) time

Jan 1, 1955

By William B. Plank

ENGINEERING students to the number of 73,269 had been enrolled in United States and Canadian schools on Nov. 5, 1945, but, as shown in the following tables, even this sizable number will not greatly remedy the 150,000 deficit reported by Vannevar Bush, director of the U. S. Office of Scientific Research and Development, to exist in the engineering and scientific man-power supply. These figures were received in advance from the Society for the Promotion of Engineering Education, and are given in detail in the January 1946 issue of the Journal of Engineering Education. Although the enrollment on Nov. 5 was an increase of 76% over the low of 41,632 in 1944-45, it was still 36% below the peak enrollment in 1941-42 of 115, 228. These figures include both undergraduate students and graduate students in the schools of the United States and Canada and are therefore comparable. As was to be expected, almost half of this enrollment is in the first or freshman year and 25% of the total are veterans. Also, 1,850, or about 2.5%, are women. A measure of the seriousness of the engineering graduate supply in these two countries is indicated by the trend of the number of first degrees that have been conferred during this period of scarcity:

Jan 1, 1946

By C. W. Kovach, A. Moskowitz

Studies were undertaken to investigate the effects of manganese content on the machinability and other Properties of a free machining martensitic stainless steel (AISI Type 416). Machinability was found to be significantly improved in steels of high manganese content, and a direct relationship was obtained between machinability and steel Mn:S ratio. As the manganese content of the steel increases, the sulfide Phase present changes from CrS to (FeMn)Cr2S4 to (MnFeCr)S, and finally to MnS. The average sulfide inclusion hardness decreases through the same range of increasing manganese content. The mechanism for machinability improvement is discussed in terms of a soft ductile sulfide affecting deformation in the secondary shear zone. Type 416 containing relatively high manganese for improved machinability shows good general properties. The effects of increasing manganese content on mechanical properties, cold formability, and corrosion resistance are described. THE addition of sulfur is commonly used to improve the machinability of stainless steels. However, little attention has been paid in the past to the composition and characteristics of the sulfur-containing phase or phases present in these resulfurized steels. Recent information on the properties of sulfide phases, and their role in metal cutting, suggests that variations in these phases could have critical effects on machin-ability, as well as important effects on formability and other properties such as corrosion resistance. Manganese, chromium, and iron are strong sulfide forming elements present in stainless steels! of these, manganese has the greatest sulfide forming tendency and iron the least.1"1 The manganese content of resul-furized 13 pct Cr steels, often about 0.5 pct, can be insufficient or only barely sufficient to combine with the sulfur that is present; thus, the precise level of manganese can strongly influence the nature of the sulfide phase. Sulfide phases which may be present in stainless steels have been reported to include CrS, a spinel-type sulfide, chromium-rich manganese sul-fide, and manganese Sulfide.5,6 Detailed phase relationships for the Fel3Cr-Mn-S system have been reported by the present investigators,7 and a portion of this work will be referred to subsequently in this paper. Recent work by Kiessling6 and Chao et a1.8 has shown that sulfide phases can display wide variations in hardness, and may undergo considerable plastic deformation under isostatic loading.9-12 Early theories of metal cutting attributed the influence of sulfur to a lubricating effect. It is now apparent that the influence of the nonmetallic inclusions and their properties on crack initiation, deformation in the shear zones, and boundary films must also be considered in relation to the machining process. This paper presents the results of studies conducted to relate machinability to the various sulfide phases which occur in stainless steels. This work has led to the development of alloys with improved machinability, and has generated information on the effects of inclusions on metal cutting processes. Effects of sulfide inclusions and steel composition on other important metallurgical properties are also discussed. MATERIALS For drill machinability and inclusion studies, 10 lb laboratory heats were melted in an air induction furnace. These heats were made with sulfur contents be tween 0.10 and 0.50 pct and manganese contents be tween 0.05 and 3.0 pct. Residual elements were added to the heats in amounts typical for commercial steels. The typical compositional range covered by the heats is shown below: C Mn P S Si Ni Cr Mo Cu N 0.10 0.05 0.007 (M0 0.40 0.40 13.0 0.20 0.10 0.03 3.0 0750 The laboratory ingots were forged in the temperature range of 1800" to 2100°F to 3/4-in. sq bars, and all bars tempered to a hardness aim of 200 Bhn prior to testing. Because of differences in composition and tempering response, the tempered bars showed some variation in hardness (175 to 275 Bhn) as well as variations in delta ferrite content (0 to 50 pct). Composition, hardness, and delta ferrite content were considered in the analysis of the machinability data. Additional tests involving tool-life evaluation and determination of other properties were conducted on materials from commercially melted and processed 15-ton electric furnace heats. TESTS AND PROCEDURES Machinability of the laboratory heats was evaluated in a drill test. In this test, 1/4-in. diam holes, 0.4 in. deep, were drilled alternately in a test bar and in a standard bar for a total of four holes in each. This sequence was repeated three times using a freshly sharpened drill each time. The average time required to drill a hole in the test bar was compared to that for the standard bar. A drill machinability rating was assigned to the test bar relative to a rating of 100

Jan 1, 1970

By E. M. Cox, A. S. Skapski, N. H. Nachtrieb, M. C. Bachelder

As a result of using copper-containing scrap in the steelmaking process, the copper content of steels has been steadily increasing for years. Consequently the possible role copper may play in the steelmaking process and in the finished product begins to attract the metallurgists' attention. Some time ago one of the present authors forwarded the idea—based on the results of the analysis of nonmetallic inclusions extracted electrolytically from steels—that sulphur in plain carbon steels is distributed mainly between copper and manganese, the amount of iron sulphide being very small; and that, consequently, the problem of copper and that of sulphur in steel cannot be treated separately.' At the time of the publication of the quoted paper little was known about the relative affinities of copper and manganese for sulphur at high temperatures except that at moderate temperatures (below 1000°C) the affinity of manganese for sulphur is much greater. To gather more experimental data on this subject, the present authors undertook the investigation of the equilibrium constants of the reactions: 2Mn(8 or 1) + S2(g) = 2MnS(s) 4Cu(s or 1) + S2(g) = 2Cu2S (S or I)* 2Fe(s) + S2(g) = 2FeS (s or 1) over a range of temperatures wide enough to establish the dependence of these equilibrium constants on temperature. From the equilibrium constants (K = l/Ps2) the free energy of formation (affinity) can be calculated from F° = -RTln 1/PSt (1) where the standard conditions chosen are: 1 atm of sulphur pressure and the activities of condensed components equal one. The decomposition pressure, Ps2, of sulphur over the respective sulphides is too small to be measured directly, but there is a way of eliminating this difficulty by measuring the equilibrium constant of the reaction between the sulphide and hydrogen. From the latter and from the equilibrium constant of the thermal dissociation of H2S we then calculate Ps2 for the respective sulphide. 2Mn + 2H2S = 2MnS + 2H, 2H2 + S2 = 2H2S_________ 2Mn + S2 = 2MnS The numerical values of the equilibrium constant of the thermal dissociation of H2S at different temperatures were taken from Kelley's paper, "The Thermodynamic Properties of Sulfur and its Inorganic Compounds."² In previous experimental work published by Jellinek and Zakowski3 and by Britzke and Kapustinsky4 the equilibrium constants of the reactions Metal sulphide + H2 = H2S + metal were determined by passing hydrogen, at different rates of flow, over the sulphide, analyzing the resulting H2S + H2 mixture and then extrapolating the H2S/H2 ratio (which is a function of the rate of flow) to the zero speed of flow, a method necessarily involving considerable uncertainty. In the present work the equilibrium ratio was actually measured instead of being extrapolated. The apparatus is shown in Fig 1. Experimental Procedure The sulphides were prepared by the following methods: FeS Powdered iron which had been reduced with hydrogen (ferrum reduc-tum) was mixed in stoichiometric ratio with sublimed sulphur and carefully ground. The mixture was put into an alundum crucible, covered with pure sulphur, and the reaction started by touching the mixture with a glowing iron rod. After the reaction was completed the product (still containing some metallic iron) was again ground with sulphur, put into a Rose crucible, covered with sulphur, and heated in a strong current of pure hydrogen. Analysis of the final product showed 62.46 pct Fe and 36.59 pct S. Theoretical for FeS: 63.53 pct Fe and 36.47 pct S. MnS Manganese sulphide (precipitated and carefully washed with distilled water containing H2S) was dried in a Rose crucible in an atmosphere of H2S and heated in a current of hydrogen for 2 hr at red heat. The product was then ground and ignited for several hours at 1000°C in a current of hydrogen sulphide. Analysis showed 64.53 pct Mn and 36.63 pct S. Theoretical: 63.15 pct Mn and 36.85 pct S. Some MnS samples were prepared from metallic manganese and sublimed sulphur by mixing and grinding them and then heating in a current of hydrogen sulphide in an alundum tube.

Jan 1, 1950

By Alfred Weiss

When I first received the announcement of this meeting I was pleased to see that this 14th APCOM Symposium had expanded its range of interest. One new topic to be considered this year is long range or strategic planning--the continuous process by which current risk taking decisions are made systematically, and with the greatest knowledge of future impact. Long range planning should receive our attention. It is the first step in the management process and the foundation of many--if not all --key managerial decisions. Improvements made at this stage of managing are almost certain to be of benefit in later stages of decision making. It is obvious to many of us that in a physical process such as mineral beneficiation, one does not concentrate all of one's attention on the flotation design without also considering the grinding, cycloning, and desliming stages of the process. Taking this a step further it would be equally erroneous to find a mineral engineer designing a mill without due consideration for mine, smelter and refinery and beyond that the sales goals, growth and profit objectives of the firm itself. And yet, how many times have we seen organizations staff and reorganize without consideration of an overall plan; without adherence to the management process which by its definition, calls for a plan first, followed by the appropriate organization and staff. The computer applications traditionally discussed at APCOM meetings have concentrated on areas dealing with things and people-- the implementation of the plan, rather than with concepts and ideas, the formulation of the plan.

Jan 1, 1977

By Jr. E. H. Dix.

In selecting the subject, "Acceleration of the Rate of Corrosion by High Constant Stresses,'' for the 1940 Institute of Metals Division Lecture, I have been influenced by its highly theoretical and speculative nature as well as by the great practical importance of the correct interpretation and appraisal of the engineering significance of the phenomenon. I lay no claim to originality in talking on this topic, since it has been the subject of discussion for over a quarter of a century. However, as our technical thinking advances, old phenomena take on new and more significant aspects. In our studies at the Aluminum Research Laboratories, we have encountered many perplexing and seemingly contradictory results and have been fascinated by the problem of dovetailing all of the many pieces of information to make a complete picture. I hope that in the brief period of this lecture I may share with you some of the enjoyment we have had in attempting to meet this challenge to metallurgical science. The emphasis generally has been placed on the spontaneous failure by cracking of a metal under the combined action of high stress and corrosion, hence the present-day use of the terms "stress corrosion" or "stress corrosion cracking." The older term "season cracking," applied more specifically to copper-base alloys, includes, by inference, the element of time. For the purpose of the discussion today I will use "stress corrosion" to cover broadly the effect of stress in accelerating the rate of corrosion of metals. To stay within the limits of allotted time the disrussiorl will cover the effect of high static stresses rather than repeated or dynamic stresses, which would take us into the related field of corrosion-fatigue. The subject is particularly appropriate for an Institute of Metals Division Lecture because much the same phenomenon has been observed in almost all metal systems. Thus, in addition to the season cracking of brass may also be mentioned the "caustic embrittlement" of steel boiler

Jan 1, 1940

By Jr. E. H. Dix.

In selecting the subject, "Acceleration of the Rate of Corrosion by High Constant Stresses,'' for the 1940 Institute of Metals Division Lecture, I have been influenced by its highly theoretical and speculative nature as well as by the great practical importance of the correct interpretation and appraisal of the engineering significance of the phenomenon. I lay no claim to originality in talking on this topic, since it has been the subject of discussion for over a quarter of a century. However, as our technical thinking advances, old phenomena take on new and more significant aspects. In our studies at the Aluminum Research Laboratories, we have encountered many perplexing and seemingly contradictory results and have been fascinated by the problem of dovetailing all of the many pieces of information to make a complete picture. I hope that in the brief period of this lecture I may share with you some of the enjoyment we have had in attempting to meet this challenge to metallurgical science. The emphasis generally has been placed on the spontaneous failure by cracking of a metal under the combined action of high stress and corrosion, hence the present-day use of the terms "stress corrosion" or "stress corrosion cracking." The older term "season cracking," applied more specifically to copper-base alloys, includes, by inference, the element of time. For the purpose of the discussion today I will use "stress corrosion" to cover broadly the effect of stress in accelerating the rate of corrosion of metals. To stay within the limits of allotted time the disrussiorl will cover the effect of high static stresses rather than repeated or dynamic stresses, which would take us into the related field of corrosion-fatigue. The subject is particularly appropriate for an Institute of Metals Division Lecture because much the same phenomenon has been observed in almost all metal systems. Thus, in addition to the season cracking of brass may also be mentioned the "caustic embrittlement" of steel boiler

Jan 1, 1940

By H. I. Aaronson, C. Wells

Configurations of ferrite crystals have been found in a plain carbon steel which appear to have resulted from the nucleation of new ferrite crystals at the interphase boundaries of previously formed crystals despite the high carbon concentrations which necessarily develop at these boundaries. This phenomenon has been termed sympathetic nucleation. An attempt has been made to reconcile the occurrence of sympathetic nu-cleation with current nucleation theory. THIS investigation is one of a series on the formation of proeutectoid ferrite from austenite. From the viewpoint of chemical composition, this reaction consists of the nucleation and diffusional growth of crystals of carbon-poor ferrite within a matrix of carbon-rich austenite. The austenite adjacent to the austenite-ferrite boundaries will be greatly enriched in carbon, approximately to the value of the y/(a + y) equilibrium curve or its metastable extrapolation at the temperature of transformation. Those areas of austenite appreciably farther removed from the growing ferrite, on the other hand, will be relatively unaltered in composition, especially at the earlier stages of transformation. Since rates of nucleation are considered to decrease exponentially with decreasing supersaturation,' the frequency with which ferrite nuclei appear at austenite-ferrite boundaries should be negligible in relation to that at which they form in other regions of the austenite. During this investigation, however, many groupings of ferrite crystals have been found which appear to have resulted from the nucleation of ferrite at austenite-ferrite boundaries. This phenomenon has been given the name of sympathetic 71.1tcleation. A number of micrographs of morphological configurations caused by sympathetic nucleation will be presented, after which an explanation for this reaction will be proposed in terms of current nucleation theory. Some of the structures to be considered are composed of bainite, an aggregate of ferrite and carbide, rather than of ferrite. Since ferrite and bainite differ only in that bainite forms under conditions which result in the nucleation of carbides behind the advancing austenite-ferrite boundaries,' it will usually be unnecessary, for the purpose of this paper, to distinguish between the two reaction products. All studies were performed on an electric furnace steel (obtained from the Vanadium Alloy Steel Co.) containing 0.29 pct C, 0.76 pct Mn, 0.25 pct Si, 0.005 pct P, and 0.007 pct S. The alloy was cast as a 150 Ib, 7x7 in. cross section ingot and forged into bars 2x2 in. in cross section. These bars were homogenized for 48 hr at 1250°C in an Endo-Gas atmosphere. The depth to which decarburization penetrated during this heat treatment was determined by chemical and microscopic analyses and the affected metal was removed by machining. Specimens for isothermal transformation studies were cut from the remaining material; most of these specimens were 1/2x1/4X1/16 in., though some with a thickness of 1/32 in. were prepared for use at the shorter reaction times and lower reaction temperatures. Specimens were austenitized for 30 min at 1300°C, isothermally reacted for various times at temperatures ranging from 775" to 475 "C, and then quenched in iced water. The austenite grain sizes within individual specimens ranged from ASTM Nos. 1 through —4. A commercial heat-treating salt which was continuously deoxidized by an immersed graphite crucible served to minimize the loss of carbon during austenitizing; thick covers of powdered graphite and immersed graphite rods effectively prevented decarburization in the lead pots employed for the isothermal reaction treatments. The heat-treated specimens were sectioned and mounted in Bakelite. Following the completion of standard grinding and mechanical polishing procedures, the specimens were electrolytically polished with a Buehler-Waisman apparatus and etched in 2 pct nital. Experimental Results Rules of Evidence for Sympathetic Nucleation—On the basis of observations made on a single plane of polish, one precipitate crystal may be considered to have been sympathetically nucleated at the inter-phase boundary of another precipitate crystal when the following conditions are fulfilled: 1) The sympathetically nucleated crystal is not in contact with a grain boundary or a subboundary in the matrix phase. 2) The shape, size, and location of the crystal at whose boundary sympathetic nucleation occurred (hereafter termed the base crystal) and the crystal formed by sympathetic nucleation substantially pre-clude the possibility that the plane of polish em-ployed may have concealed the fact that both crys-tals actually nucleated at a grain boundary or a sub-boundary in the matrix phase.

Jan 1, 1957

By Thomas Cox

This paper makes no claim to any new idea; it simply reviews the Treasury Department Regulations pertaining to the practical application of depreciation and depletion and other allowances governing taxation of oil and gas properties. Other methods may be existent, but as they may not conform to the legal status they must be discarded. In complying with the present laws governing the industry with regard to taxation and the allowable deductions therefrom, the following considerations are essential: Depletion, depreciation, amortization, other allowances, and items not, deductible. It is definitely understood that depletion is the loss or exhaustion sustained in the continuous operating of an oil and gas property, and that each unit of oil or gas taken out reduces the value of the property until its final exhaustion. Depletion applies only to the natural deposits of oil and gas due to their removal in the course of exploitation of any property. Depreciation is defined to cover the waste of assets due to exhaustion, wear and tear, and obsolescence of the physical property, and is separate and distinct from depletion; its allowance is that amount which should be set aside for the taxable year in such sums as for the useful life of the property will suffice to repay its original cost—or its value as of Mar. 1, 1913, if acquired by the taxpayer before that date—less the salvage value at the end of such useful life. Amortization is allowed for such facilities as were built or acquired on or after Apr. 6, 1917, for the production of articles contributing to the prosecution of the war and, in the case of vessels, those built and acquired after that date. The amount to be extinguished, in general, is the excess of the unextinguished or unrecovered cost of the property over its maximum value under stable post-war conditions. Claims for amortization must be unmistakably differentiated in the returns from all other claims of depreciation. The taxpayer is also required to furnish full information with the claims for amortization to the full satisfaction of the Commissioner. Further reference is directed to the specific rules and regulations for making these claims.

Jan 1, 1921

By H. R. Cooper, T. S. Mika

T. S. Mika (Department of Mineral Technology, University of California, Berkeley, Calif.) - Dr. Cooper's attempt to establish a correlation between process behavior and operational variables on the basis of a statistical analysis after imposing a reasonable process model is a very commendable improvement on the use of standard regression techniques. However, it must be recognized that the imposition of a model has the potential of yielding a poorer representation if its basic assumptions or mathematical formulation are invalid. It appears that at least two aspects of his treatment require some comment. First, the limitations on the kinetic law where xta represents a hypothetical terminal floatable solids concentration (cf. Bushell1), should be mentioned. Most current investigations2-9 appear to utilize the concept of a distribution of rate constants rather than a single unique value, k, to describe flotation kinetics. A distributed rate constant is certainly a more physically meaningful concept than that of a terminal concentration. The study of Jowett and safvi10 strongly indicates that xta is merely an empirical parameter, whose actual behavior does not correspond to that expected from a true terminal concentration. Rather than being a strictly mineralogical variable, as Dr. Cooper's treatment implies, it apparently represents the hydromechanical nature of the test cell as well as the flotation chemistry. The extension of batch cell kinetic results to full-scale continuous cell operation is a suspect procedure if the effect of such nonmineralogical influences on x,, remain unevaluated. There is evidence that introduction of a terminal concentration is necessitated by the inherent errors which arise in batch testing and are eliminated by continuous testing methods.' Possible lack of validity of the author's use of Eq. 1 is indicated by two unexpected results of the statistical analysis of his batch data. The first is the apparent corroboration of the assumption that the rate constant, k, is independent of particle size, i.e., of changes in the size distribution of floatable material. This assumption directly contradicts numerous results 2,4,11-l8 for cases where first order kinetics prevailed and ignores the phenomenological basis for the analysis of flotation in terms of a distribution of k's. It must be recognized that, if the rate constant is size dependent, the lumped over-all k would be time dependent; Eq. 1 would then no longer be valid. Cooper's x,, is determined by batch flotation of a distribution of sizes for an arbitrary period of time. If the size dependence of k is artificially suppressed, x,, will become a function of the experimental flotation time used in its determination. Upon reviewing the rather extensive literature concerning batch flotation kinetics, there appear to be few instances where constant k and x,, adequately adsorb variations in floatability due to particle size. The second surprising result is the low values of the distribution modulus, n, determined. Contrary to Cooper's assertion, most batch grinding (ball or rod mill) products yield values of n > 0.6, which increase as the material becomes harder.'' It is likely that the values of n = 0.25 and n = 0.42 for Trials 1 and 2, respectively, are completely unreasonable, and even the value n = 0.54 obtained for Trial 3 is unexpectedly low. Possibly, this indicates inherent flaws in the three trial models considered, in particular the assumed particle size independence of the rate constant, k. The above does not necessitate that Eq. 1 (and the terminal concentration concept) is invalid; it could constitute a good first approximation. However, the qualitative arguments used by Dr. Cooper in its justification are somewhat frail and require verification, particularly since much of the flotation kinetics literature is in opposition. Apparently, no effort was made to test these hypotheses on the actual data; in fact, since they pertain to a single batch test time, his data cannot be utilized to evaluate the kinetics of flotation. To evolve a control algorithm on the basis of this infirm foundation seems a questionable procedure. Another difficulty in his analysis arises in consideration of the froth concentrating process. As Bushel1 ' notes, for Eq. 1 to be valid it is necessary that the rate of recycle from the froth be directly proportional (independent of particle size) to the rate of flotation transport from the pulp to the froth, a restrictive condition." Harris suggests that it is more realistic to assume that depletion occurs in proportion to the amount of floatable material in the pertinent froth phase volume (treating that volume as perfectly mixed).12,21,22 The physical implications of

Jan 1, 1968

By J. M. Callow

THe results obtained by pneumatic flotation throughout the country on all classes of ore, and the tonnage now being treated by this particular method, speak for themselves. Its advantages over the so-called agitation process are now established by facts and data from practicc. The comparative efficiency of a rapidly revolving paddle, as a means for aerating an ore pulp, and of a cyeloidal or turbine blower for the same purpose, would seem to be so obvious as to leave no room for discussion. Practitioners in this art are to be congratulated on the acquisition of the valuable literary contributions that have recently been made on the theory of flotation by Messrs. Ralston, Van Arsdale, Taggart and Beach, and others, and the very valuable and able articles by Messrs. Laist and Wiggin on "Flotation Concentration at Anaconda, Mont.," by Dr. Rudolf Gahl on the "History of Flotation at Inspiration," and by David Cole on "The Advent of Flotation in the Morenci District." It is not within the province of this article to attempt an answer to the various issues raised in regard to the theory, or to defend the one advanced by me a year ago. But since discussion usually benefits the profession, a reply will be made to some of the statements made by the last-named writers. CoMPABATIVE SENSITIVENESS AND ATTENDANCE Concerning the article, "Flotation Concentration at Anaconda, Mont.," by Laist and Wiggin, a little explanation is in order. It should be stated that, with the exception of about 24 days at the end of the testing period, the Callow experimental plant at Anaconda was not run under my direction. This perhaps accounts for some of the concIusions drawn on page 499 of the descriptive paper. The conclusion that the use of acid seems to be of considerable advantage, calls for some comment. While the tests conducted by the Anaconda Copper Co. do show acid to be of considerable benefit, this is a consequence of using acid sludge as a flotation agent. My belief has always been that the Anaconda

Jan 1, 1917

By O. G. Kiel, G. W. Swift

The concept of "a continuous succession of steady-states", which has been applied successfully by Aromfsky and Jenkins to obtain a solution for the nonlinear partial differential equation describing the transient Darcy flow of gas through porous media, is demonstrated to be equally valid for transient non-Darcy flow. A mathematical model, which numerically solves the partial differential equation, is used to check the validity of the succession of steady-states solution. Comparison of sand-face pressure histories compelted by the two methods shows excellent agreement. The utility of the succession of steady-states solution in predicting performance of gas wells rests in the fact that no special computation equipment is required. The development of the succession of steady-states solution leads also to a practical method for determining and analyzing field test data. A method for taking gas-well test data under constant-rate conditions is presented. Experimental data obtained in the field by employing the constant-rate method are presented and analyzed in accordance with the succession of steady-states solution. Analysis of data in this fashion is demonstrated to give direct "in situ" information for reservoir permeability, porosity and turbulence or non-Darcy coefficient. INTRODUCTION The economics of gas production are dependent upon the transient behavior of flow within the reservoir. For production from a finite reservoir, the transient flow behavior can be subdivided into two parts. At first, the transient caused by the movement of the pressure "wave" into the reservoir is of importance. Later in the production history, the pressure-wave movement ceases and the second transient stage of material depletion becomes controlling. For reservoirs of relatively high permeability, it can be shown that the pressure wave moves into the reservoir and stabilizes quite rapidly. In the case of relatively impermeable reservoirs, quite the opposite is true. Although it is theoretically possible to compute the production capability of a well from the properties of the reservoir as determined by static tests and core analyses, more reliable information is obtained by conducting flow tests on the well and thereby obtaining some measure of "in situ" formation properties. For gas wells, there are two basic types of tests in existence: the flow-after-flow method,' and the isochronal method.' Both of these techniques are tailored to obtain data that can be analyzed in accordance with the empirical performance equation: In addition, the isochronal method makes provision for the sluggish nature of pressure-wave movement in "tight" formations by requiring pressure build-up between flows and by stipulating that data obtained on successive flows be analyzed at equal elapsed flow times. It can be demonstrated that either test is valid for reservoirs of high permeability. Further, since it has been pointed out that the pressure wave stabilizes rapidly for reservoirs of this type, tests of relatively short duration will give stabilized information on the performance of a well. Further decline of sand-face pressure and/or production rate may be determined by employing material-balance techniques. Cullender' points out that for relatively impermeable reservoirs the flow-after-flow method gives invalid results. (See Appendix C.) If the isochronal method of testing is used, there are two alternatives: (1) the tests must be conducted for a sufficient length of time to obtain stabilized information (which may require months to accomplish); or (2) some method for extrapolating the results of short-term isochronal tests must be employed. The first alternative is impracticable because of manpower, conservation and economic considerations. Recourse to the second alternative requires some assurance regarding the reliability of the extrapolation technique. Poettmann and SchilsonJ present an empirical method for predicting stabilized performance. The present investigation was originally initiated to determine the reliability of this technique. To do this, a mathematical model was developed to simulate the Darcy and non-Darcy flow of gas through porous media. The model consisted of a finite-difference approximation of the nonlinear partial differential equation which was solved on an IBM 7090 computer. Long-term production histories were simulated by the model and compared against predictions obtained from the Poettmann-Schilson method. As the work progressed, it became apparent that a straightforward predictive equation could be developed by utilizing the concept of a succession of steady-states. As a result, the emphasis of the work was redirected to exploit the advantages of the new method.

By John W. Chandler

INTRODUCTION Where and how to spend the exploration dollar to net the greatest economic return, has always been a major problem for mining companies. Minerals are being consumed in ever increasing quantitie: throughout the world and the mining industry is being called on to meet this demand. In view of the present world-wide nationalistic trend, it is becoming more difficult to determine where exploration money can be spent most profitably. An exploration project should be evaluated continually--in the beginning, to define economic targets and later to determine, as early as possible, whether a project has a chance of developing into a venture that will make a profit acceptable to top management. At this point, a decision can be made whether or not to proceed with plans to bring in a new mine. Exploration, evaluation, and development, therefore, must be fully integrated in transforming an exploration project into a profitable mining venture. DEMAND FOR LEAD AND ZINC Lead and zinc are metals basic to our economy and the demand for them will continue to rise as the population in the world increases. If the population continues to grow at the present rate, it will about double by the year 2000. The accelerating demand for these metals is shown by statistics. Nearly half as much lead (48%) and more than half as much zinc (55%) have been mined between the two world wars as in all pre- ceding history. (1)

Jan 1, 1970

By Harry L. Washburn, Robert L. Llewellyn, W. J. Halvorsen

Many of the problems that occur in the preparation plant originate from practices in the mine. Impurities in raw coal can be in the seam itself or from extraneous material taken in mining from the roof or bottom. In the case of underground mines, the choice of mining equipment will affect the size consist and the amount of extraneous material included with the coal. Also, governmental regulations concerning the degree of rock dusting, gobbing underground, and cleanup have increased the dirt in raw coal. Sulfur dioxide emission standards, on the other hand, are pressuring the coal industry to clean coal more thoroughly. Coal supplied for coking purposes is nearly all upgraded by washing, while for the largest market, electric power generation, a high proportion is shipped as a raw product with processing, in whole or in part, only necessary when excess impurities are mined with the coal. This chapter will deal primarily with plants that process or wash coal to some extent (Fig. 1) and only incidentally with mines shipping raw run-of-mine coal crushed to a top size of, usually, 51 to 102 mm (2 to 4 in.), with little, if any, other treatment. JUSTIFICATION FOR COAL PREPARATION During the past decade, major changes have occurred affecting the market, profit, and long-range planning of the coal industry. Mining companies have become "partners" with consumers at many new and some old mines, both for steam and metallurgical coals. Coal properties have become "assigned" tonnages at mutually agreed upon conditions and prices. Lower unit-train tariffs have been instrumental in helping coal markets to compete against oil and nuclear energy. Coal prices for power plants are still on a Btu (British thermal unit)

Jan 1, 1981

By Ronald K. Linde

Metastable Ag-Cu solid solutions at two compositions beyond the maximum limits of solubility obtainable by quenching from the solid state were obtained by rapid quenching from the liquid state. The process of transformation of the metastable solid solutions into the equilibrium phases was studied by means of X-ray diffraction intensity measurements and electrical-resistance measurements; metallographic examination was also performed. Results are compared with those for an alloy quenched from the solid state at a composition which exists as a solid solution at elevated temperatures. Activation energies for the trans-formation were computed to be 33,600 * 2500 and 33,100 * 2000 cal per g mole for the 60.1 and 75.0 at. pct Ag;Cu compositions, respectively THE kinetics of precipitation in supersaturated solid solutions obtained by quenching from high temperature has been thoroughly studied in many alloys, and detailed investigations of the early stages of nucleation and subsequent growth of the equilibrium phases have been carried out. All of these studies have been made on alloys quenched from the solid state, however, and it is the purpose of this paper to present some of the results on the kinetics of transformation of metastable solid solutions in Ag-Cu binary alloys whose compositions lie outside of the solid-state limits of solubility. Limits of solubility in the solid state can be increased by rapid quenching from the liquid state. This was first demonstrated by Falkenhagen and Hofmann, who obtained appreciable increases in solubility limits of the elements of the first transition series in aluminum by rapid cooling of liquid alloys through contact with a copper mold maintained at liquid nitrogen temperature.' The same basic idea of cooling a liquid alloy by conduction onto a substrate rather than by convection of a gas or liquid (conventional quenching) has been recently revived and extended to very high rates of cooling by Duwez and his collaborators. The new technique was first applied to Ag-Cu alloys because the existence of a eutectic in this system is not predicted by the Hume-Rothery rules of alloy phase formation. Rapid quenching from the liquid state resulted in metastable solid solutions at all concentrations. The kinetics of decomposition of these metastable solid solutions containing 60.1 at. pct Ag;Cu (eutectic composition) and 75.0 at. pct Ag;Cu is the subject of the present paper. EXPERIMENTAL TECHNIQUES Alloys were made in 10- to 20-g heats using silver of purity 99.99 pet and copper of purity >99.999 pct. Components were weighed accurately to 0.1 mg and melted by induction heating in an alumina crucible under an atmosphere of hydrogen. Weight losses amounted to less than 0.02 ~ct in all cases. Rapid cooling from the liquid state was achieved in an apparatus of the type described by Pietrokowsky. 3 In this technique a freely falling drop of molten alloy is caught between a stationary anvil and a fast moving piston, both anvil and piston being lined with copper. The resulting foils were approximately circular (about 2 cm in diam) and from about 50 to 150 u in thickness, depending on the pressure driving the piston. Metallographic samples were prepared for polishing by edge-mounting foils in Quickmount. The mostef-fective etching procedure was found to be: 10 parts NH4OH (concentrated), 1 part H2O2 (30 pct), 5 parts H2O, swab for 5 to 10 sec. The transformation of the metastable alloys to equilibrium was followed by X-ray diffraction and electrical-resistivity measurements. The peak intensity and the integrated intensity of suitable Bragg reflections of the metastable and stable solid solutions were studied with a Norelco dif-fractometer, using nickel-filtered copper KO radiation. The peaks were step-scanned at intervals of 0.05 deg. Using either a Kelvin bridge or a null circuit with a Leeds and Northrup K-2 potentiometer, the changes in electrical resistance due to phase transformation were measured for specimens cut into strips about 20 mm long and 4 mm wide. All resistivity measurements were carried out at liquid-nitrogen temperature. The isothermal heat treatment was accomplished by sealing the samples in argon-filled aluminum containers with stainless-steel O-rings. Containers were then suspended in wax baths with temperatures in the

Jan 1, 1967

By Alexander Sattman, Anton Homatsch

Jan 1, 1894

By S. Yukawa, M. J. Sinnott

A high resolution autoradiographic study of the diffusion of a nickel isotope (NP3) into copper in the temperature range of 650° to 925°C, with particular emphasis on grain boundary diffusion, has been made. The extent of grain boundary diffusion is a function of the grain boundary angle and the diffusion temperature. The ratios of the grain boundary diffusion coefficient to the lattice diffusion coefficient ranges from 104 to 105. The activation energy for grain boundary diffusion decreases with increasing grain boundary angle. STUDIES and reviews&apos;-8 of metallic diffusion have indicated that grain boundary diffusion is a common phenomenon but quantitative studies of the many variables involved are not numerous. The present work was concerned with determining the influence of the crystallographic orientation of the grain boundaries and the temperature on the extent of boundary diffusion of nickel into copper. The study involved essentially three steps: 1—the production of grain boundaries of known crystallographic orientation, 2—the determination of the extent of diffusion into the boundaries, and 3—the analysis of the resulting data in terms of the usual diffusion concepts. The grain boundaries investigated approximated the simple tilt variety having l° of freedom. They were produced by controlling the solidification from a melt of Cuprovac (a high purity vacuum-melted copper obtained from Vacuum Metals Corp.) of a pair of seed crystals so that the bicrystals of copper produced had a common <100> axis. By rotating one seed crystal relative to the other, a simple tilt boundary was produced. The angle of rotation between the two crystals is the grain boundary angle 8, or what is sometimes termed the misfit angle. In all, some 16 boundaries ranging from 2" to 72" in 5" to 10" steps were investigated. The crystallographic orientations were measured with the use of both X-ray and optical goniometric techniques. The <100> axes in the crystals were found to be parallel within 2" to 3" with the exception of one crystal (8 = 12") in which the axes were 6" from being parallel. All bicrystals showed evidences of sub-grain structures. Laue analyses showed that these subgrains differed in orientation up to a maximum of 2". Because of these variations, and some curvature in the boundaries, the grain boundary angles listed are actually average values and deviate from the 1 o of freedom boundaries. The stripping film technique of high resolution autoradiography was used to detect the diffusion of the nickel isotope into the grain boundaries of the bicrystals of copper. Kodak experimental permeable stripping film with an emulsion layer 5 u thick

Jan 1, 1956

By J. T. Mackenzie

Henry Marion Howe, in whose memory we are gathered together, was one of the great thinkers who develop from time to time to whom is given the rare gift of synthesis. Analysis is given to few, but synthesis, the ability to show the relation of all parts to each other and thus to give a clear picture of the whole, is reserved for the very few. Analysis can be achieved by honesty, intelligence, and industry, but synthesis is only given to genius. Professor Howe&apos;s crowning achievement is the picture of the whole iron-carbon series shown in Fig. I, which places steel, malleable, gray iron, mottled and chilled irons in their proper relation to each other and shows the essential unity of the series. Perhaps his best statement of the case is found on page go of the Metallography of Steel and Cast Iron in these words: " Each member of the gray cast-iron series consists of the metallic matrix approximately equivalent to that member of the steel-white-cast-iron series to which it corresponds in percentage of combined carbon with its continuity broken up—by masses of graphite ..." Apparently he had taken considerable interest in this idea around the turn of the century, for he refers to a discussion at the Franklin Institute in I900 in which he said: "Though many others had probably conceived this relation between the steels and cast irons, it was here enunciated for the first time, so far as I know. It was received with great incredulity." The concept was explained in some detail in a paper on "The Constitution of Cast Iron" presented before the A.S.T.M. in 1902 when Professor Howe was retiring president of that young society. In the discussion Dr. Sauveur stated that he was "very well acquainted with Professor Howe&apos;s theory of the constitution of cast iron," and went on to say that while he "shared it to the fullest extent, some foundrymen . . . claim cast iron is a metal entirely different from steel . . . that steel and cast iron have very little in common, and that therefore the knowledge gained in the study of steel is of little or no value in the study of cast iron." Dr. Moldenke, in discussing the same paper, said he had been working on the same theory for 12 years but he laid no claim to publication. Discussing the difference in the micro-structure of the metallic matrix, Professor Howe pointed out that "such minor structural differences are indeed to be expected, because of the difference in the conditions under which these constituents are generated. "One difference in these conditions is that the steel of most micrographs has been either forged or at least treated thermally in such a way as to give a new structure radically different from that which formed during the initial solidification, whereas the cast irons have not. Hence what we see in the steels is a transformation structure, but in the cast irons a solidification structure. By giving the cast

Jan 1, 1944

By J. T. Mackenzie

Henry Marion Howe, in whose memory we are gathered together, was one of the great thinkers who develop from time to time to whom is given the rare gift of synthesis. Analysis is given to few, but synthesis, the ability to show the relation of all parts to each other and thus to give a clear picture of the whole, is reserved for the very few. Analysis can be achieved by honesty, intelligence, and industry, but synthesis is only given to genius. Professor Howe&apos;s crowning achievement is the picture of the whole iron-carbon series shown in Fig. I, which places steel, malleable, gray iron, mottled and chilled irons in their proper relation to each other and shows the essential unity of the series. Perhaps his best statement of the case is found on page go of the Metallography of Steel and Cast Iron in these words: " Each member of the gray cast-iron series consists of the metallic matrix approximately equivalent to that member of the steel-white-cast-iron series to which it corresponds in percentage of combined carbon with its continuity broken up—by masses of graphite ..." Apparently he had taken considerable interest in this idea around the turn of the century, for he refers to a discussion at the Franklin Institute in I900 in which he said: "Though many others had probably conceived this relation between the steels and cast irons, it was here enunciated for the first time, so far as I know. It was received with great incredulity." The concept was explained in some detail in a paper on "The Constitution of Cast Iron" presented before the A.S.T.M. in 1902 when Professor Howe was retiring president of that young society. In the discussion Dr. Sauveur stated that he was "very well acquainted with Professor Howe&apos;s theory of the constitution of cast iron," and went on to say that while he "shared it to the fullest extent, some foundrymen . . . claim cast iron is a metal entirely different from steel . . . that steel and cast iron have very little in common, and that therefore the knowledge gained in the study of steel is of little or no value in the study of cast iron." Dr. Moldenke, in discussing the same paper, said he had been working on the same theory for 12 years but he laid no claim to publication. Discussing the difference in the micro-structure of the metallic matrix, Professor Howe pointed out that "such minor structural differences are indeed to be expected, because of the difference in the conditions under which these constituents are generated. "One difference in these conditions is that the steel of most micrographs has been either forged or at least treated thermally in such a way as to give a new structure radically different from that which formed during the initial solidification, whereas the cast irons have not. Hence what we see in the steels is a transformation structure, but in the cast irons a solidification structure. By giving the cast

Jan 1, 1944

By E. Gaujot

IN connection with the question of coal waste and economy in mining, we would call the attention of those interested to an apparatus invented by M. Dernencourt, Superintendent of the Anzin Division of the Anzin Coal Company, North of France. This apparatus is known in France and Belgium under the name of prop screw jack (vis botte), and has been used with good results in the above-named countries for some years past. M. Ponson gives, in his " Traité de l&apos;exploitation des Mines," a description of it (page 533), but as the description given is old, the work not widely known in this country, and as some valuable improvements have been made since, I thought it might be useful to give a description of it, having seen it in operation in 1867, while in Europe to attend the great Exposition, and on a scientific tour to the mining districts of France, Germany, Belgium, and Italy. The prop screw jack is composed of the following pieces: I. The body or column B, Fig. 4 [Plate (1)], of oak or yellow pine, sawed square, the bark taken off, and any length, proportionate to the vein. The smallest are 10 inches diameter at the base, and 9 inches at the top, the height being from 12 to 15 inches less than the size of the vein. In the axis of this column, and at the top end, is a cylindrical opening or hole, C, 2 3/4 inches diameter, 10 inches deep, for the screw, S. II. Two wrought-iron rings, R R, to strengthen the two extremities of the column ; the rings must be put on hot. III. A cast-iron washer, E, with hole in centre a little larger than the screw, to be put on the top of the column, and on which the nut is to rest; the top side of this washer must be faced on the lathe, also the bottom of the nut, to prevent friction. IV. The screw, S, having a total length of 12 inches and a diameter of 21/2 inches (for very high veins this diameter may be in¬creased to 3 inches), and has on its top a wrought-iron plate, T,

Jan 1, 1873