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By T. D. Murphy

In the fall of 1988 it became evident that the accuracy of sulfur forecasts for Monterey Coal's No.1 Mine needed to be improved. In addition, it became necessary to predict if any individual train shipments during a month would exceed a contract sulfur limit. The challenge was to develop a forecasting process that would take into account the variability of the coal in the ground as well as the difference between laboratory and preparation plant sulfur reduction efficiency, and the effects of mining coal with multiple units. This paper describes how geostatistics and simulation techniques were used to meet this challenge.

Jan 1, 1992

By D. J. McAdam

Results of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station have been presented by the author in four papers.1, 2, 3, 4 In those papers references were given to the work of Haigh in 1917.5 The investigation at Annapolis included a variety of ferrous and non-ferrous alloys. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at stresses far below the ordinary endurance limit. The experiments also showed that, for most metals, severe stressless corrosion prior to fatigue is much less damaging than even slight corrosion simultaneous with fatigue. The term "corrosion-fatigue" was restricted to mean the simultaneous action of corrosion and fatigue. The combined effect of corrosion followed by fatigue was called "prior-corrosion fatigue." A stress-cycle graph representing corrosion-fatigue is a curve approaching a horizontal asymptote, the ordinate of which may be called a "corrosion-fatigue limit." To avoid confusion in later discussion, the term "endurance limit" will be restricted to mean the fatigue limit obtained by tests in air with specimens as free as possible from stress concentration and from corrosion. The cndursnce limit as thus obtained presumably represents an inherent property of the metal.

Jan 1, 1929

By D. J. McAdam

Results of investigation of corrosion-fatigue of metals at the U. S. Naval Engineering Experiment Station have been presented by the author in four papers.1, 2, 3, 4 In those papers references were given to the work of Haigh in 1917.5 The investigation at Annapolis included a variety of ferrous and non-ferrous alloys. The experiments showed that even slight corrosion simultaneous with fatigue may cause failure at stresses far below the ordinary endurance limit. The experiments also showed that, for most metals, severe stressless corrosion prior to fatigue is much less damaging than even slight corrosion simultaneous with fatigue. The term "corrosion-fatigue" was restricted to mean the simultaneous action of corrosion and fatigue. The combined effect of corrosion followed by fatigue was called "prior-corrosion fatigue." A stress-cycle graph representing corrosion-fatigue is a curve approaching a horizontal asymptote, the ordinate of which may be called a "corrosion-fatigue limit." To avoid confusion in later discussion, the term "endurance limit" will be restricted to mean the fatigue limit obtained by tests in air with specimens as free as possible from stress concentration and from corrosion. The cndursnce limit as thus obtained presumably represents an inherent property of the metal.

Jan 1, 1929

By K Lee, L Mann, J Bygrave, G Sheldon

Ausmelt is supplying commercial quantities of an alkyl hydroxamate flotation collector AM28 for flotation of oxide and supergene base metal ores and tailings. AM28 is a non-hazardous product used as a ten per cent to 50 per cent solution in dilute potassium hydroxide. It is a selective flotation collector for oxide or oxidised base metal minerals and replaces conventional sulfidisation for oxide mineral flotation. At Radio Hill, the AM28 is used in conjunction with traditional sulfide collectors, which allows simultaneous flotation of oxide and sulfide copper minerals. The Fox Resources Radio Hill copper concentrator near Karratha, Western Australia, is currently configured to treat supergene copper ore sourced from the West Whundo open pit. This Archean VMS type copper deposit has been deformed and remobilised with uplift, erosion and weathering to form a significant supergene zone. The sulfide copper minerals present in the upper zone are digenite and chalcocite with lesser chalcopyrite and covellite. Oxide copper minerals present include cuprite, with lesser malachite and azurite. Gangue minerals include quartz, talc and chlorite. Plant trials at Radio Hill are reported for supergene West Whundo ore, where the AM28 was stage added into the circuit at nominally 80 g/t. Plant data over three months shows the copper recovery increased consistently from around 50 - 60 per cent to above 70 per cent when AM28 was added. This has been proven statistically. The grade of the concentrate was consistent with and without AM28, at nominally 22 - 24 per cent copper.

Jan 1, 2007

By Walter V. Knopp, Laurence Delisle

The aim of this work was the preparation of nickel-steels from elemental metal powders by powder metallurgy techniques. It was known that plain carbon steels could be made from a mixtufe of iron powder and graphite and that the effect of carbon on iron in powder form was of the same nature as that produced in fusion metallurgy. The problem in making nickel steels from elemental powders consisted therefore in finding out whether sufficient diffusion of the nickel and other incidental metals . normally present in such steels could be induced in the solid state to modify the properties of plain carbon steels made from powders and produce the beneficial effect of alloying. The composition selected originally was that of an S.A.E. 2330 steel. Metal powders, in the proportion correspending to that composition, were mixed with graphite, pressed, and heated at different temperatures for different periods of time, to produce bonding of the metal particles and mutual diffusion of the various elements without melting. Temperatures up to 1325°C and sintering periods as long as 6 hr were first investigated because it was expected.that such conditions would produce maximum diffusion with an accompanying improvement in the properties of the alloy. It was found that, although diffusion proceeded to a large extent under the conditions investigated, it would not be complete unless sintering were carried out at a high temperature for much longer than 6 hr. Relatively high temperatures and long sintering times are objectionable from a practical point of view, particularly when a low COSt material is to be produced, because they necessitate the use of special, costly equipment. Work could be done to improve the diffusion of iron and nickel by changing conditions other than the sintering temperature and time, that is, finer primary or alloy powders could be used. However, a marked change in the properties of the steel had been observed even with only partial diffusion. It was thought, therefore, that instead of trying to improve the diffusion, advantage might be taken of its incompleteness to produce a special structure consisting, in the unquenched condition, of a hard constituent, rich in nickel, dispersed in a tough pearlitic matrix. Steels with such a structure, not readily obtainable by fusion, should have desirable mechanical properties. Besides, it should be possible to prepare them from elemelltal powders under economical conditions. This latter alternative was therefore adopted for the second phase of this work. This report is divided into four parts: I. General Procedure. 2. Effect of Sintering Temperature. 3. Effect of Varying the Nickel Content. 4. Effect of Alloying Elements. General Procedure The general technique of cold pressing as used in powder metallurgy was applied.

Jan 1, 1949

By M. A. Grossman

THE hardenability of most steels can be predicted within 10 to 15 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter"; namely, the diameter of bar, in inches, that will just harden all the way through (absence of unhardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test. The data bring out certain features rather clearly. For example: I. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals," are known; thus an "incidental" chromium content of o.-2o per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful as would appear to be common experience; observe that an increase from no manganese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.2o per cent Mo provides a factor of 1.63, an increase of over 6o per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the first small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater harden ability will be obtained by using, for example, o.5 per cent of each than by using 1.0 per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain steels of high hardenability. It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, undissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum possible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the absence of Cr, and V up to 0.04 per cent), the charts provide reasonable approximations. The precise figures on the charts are suggested as tentative, subject to some modification as more data accumulate, but the fundamental concept appears to be supported by tests made on a wide variety of steels, a few of the correlations being shown in Fig. I.

Jan 1, 1942

By Joseph Kuti

Longwall mining is the term used for the underground extraction of a wide and deep panel of coal. Such a panel may be blocked out by one or more entries on either side ("head" and "tail") of a longwall face. If all the entries are pre-driven, the panel extraction is termed longwall retreat mining. With one exception, all the longwall faces in the United States are of this type.1 Prior to the general decline in the rates of production with Continuous Miners, the development of the multiple entries generally kept ahead of the longwall extraction rate. This is no longer the case: longwall extraction rates far exceed the rate of development. In addition to this problem, in newly established mines, the development of a haulage and bleeder system based on multiple entries results in a lead-time of three years or more before longwall mining can be applied.

Jan 11, 1979

By Mark L. Mott, Michael P. Synder

The Mine Safety and Health Administration has developed a program to improve the decision making process of personnel involved in mine emergency situations. The Mine Emergency Responsiveness Development Program (MERD) has been designed specifically for fires and explosions in underground mines. This program addresses the responsibilities and organizational requirements that are necessary during rescue and recovery operations of a mine emergency . Specific skills and knowledge are required to manage an organization of personnel under conditions of intense stress, such as a mine fire or explosion. As a result, the MERD program develops these skills by providing role playing emergency simulations. This role playing provides the participants with the opportunity to experience problems, explore solutions and interact with other personalities which may exist during mine emergency situations. This paper presents the standard procedures for the MERD program developed by the Ventilation Division of the Pittsburgh Health Technology Center.

Jan 1, 1991

By George. Petersen

"El trabajo refiere algunos aspectos del depósito de estaño en el yacimiento de Condiriquiña (Puno), como en zonas de Apurimac, Lima, Pasco, Ancash, Cajamarca del Perú. Se conoce que los principales depósitos de estaño provienen de los ramales cordilleranos de Bolivia, abarcando una serie de yacimientos. En vista de una posterior demanda del producto, fue necesario que el Perú inicie una exploración de este metal en territorios adyacentes a Bolivia. Sin embargo, las exploraciones no se concretaron más que a las inmrediaciones del lago Titicaca. Posteriormente se descubrió minerales de estaño en diversas partes de nuestro territorio,aunque que ningún depósito explorado tenga un resultado de valor económico-industrial considerable. El aspecto geoquímico del estaño no tiene relaciones con el fierro, cromo, silicio, careciendo de estaño en los depósitos líquidos magmáticos y en las rocas ígneas de naturaleza básica. Durante los procesos metalogenéticos el estaño se concentra y constituye un elemento característico de la cristalización residual; presentándose tanto en el alcance neumatolítico ácidocomo en el hidrotermal. En consecuencia, los depósitos de estaño son de origen neumatólítico, cuyas masas y filones de catiserita están asociados con un batolito de granito, de edad oligocénico. Así, las rocas encajonantes consisten en pizarras y cuarcitas de Ordovicito, se transforman en rocas greisen o ígneas. Finalmente, los depósitos estanníferos se clasifican según sus alcances genéticos en depósitos supergenos e hipogenos, los cuales se dividen en depósitos pegmatítico, neumalotílicos, de transición neumatolíticos-hidrotermales y los depósitos hidrotermales."

Jul 20, 1959

By B. B. L. Seth, H. U. Ross

A generalized rate equation for the reduction of iron oxide was derived from which two particular equations were obtained: one for rate controlled by the transportation of gas, the other for rate controlled by the phase-boundary reaction. Pellets of pure ferric oxide having diameters of 8.5 to 17.5 mm and a density of 4.8 g per cm3 were prepared and reduced by hydrogen at 750° to 900°C. From the analysis of data obtairzed, it was observed that neither the phase-houndarv reaction nor the transportation of gas controlled entirely the rate of redziction. Rather, the mechanism of reduction can he divided into three stages. In the beginning, the process seems to depend predominantly on the surJrce reaction, hut after a layer of iron is formed the diffusion of gas becomes the controlling factor. Towards the end, however, the rate falls sharply due to a decrease in porosity. The times predicted by the generalized equation for a certain degree of reduction showed an excellent agreement with those obtained experinmentally for pellets of varying sizes. WIDE interest in iron oxide reduction has resulted in many valuable studies pertaining to thermody-namical properties, equilibrium diagrams, and chemical kinetics. Although the thermodynamical properties and equilibrium diagrams are now known with a fair degree of accuracy, the mechanism and rate-controlling step in the reduction of iron oxides presents a problem to research workers which is still unsolved. This is because the field of chemical kinetics is so highly complex. Besides the chemical reaction between oxide and reducing gas, several other processes are occurring simultaneously such as solid-state diffusion of iron through intermediate oxides (FeO and Fe3O4), the diffusion of reducing gas inwards and of product gas outwards, and the sintering of iron if reduction is carried out above the sintering temperature of iron. Furthermore, there is a large number of variables, including the nature and flow rate of the reducing gas, the chemical composition and physical properties of the ore, the temperature of reaction, particle size, and so forth, all of which can affect both the mechanism and the kinetics of reduction. Despite the controversy and diversity of opinion about the mechanism of iron oxide reduction, three main schools of thought have emerged. According to the first, the rate is controlled by the diffusion of gas through the boundary layer of stagnant gas; the second claims that the rate is proportional to the area of the metal-oxide interface, while the third believes the transportation of reducing gas from the main stream to the metal-oxide interface and of product gas from the metal-oxide interface to the main stream to be the rate-controlling step. 1) The boundary-layer theory is true mainly for packed beds where the flow of gas through the bed is important. For a single particle, the boundary layer may be prevented from being the rate-controlling step if a gas flow rate of reducing gas above the critical flow rate is used. 2) Several workers have reported a linear advance of the Fe/FeO interface which provides excellent support for the belief that reduction is controlled by the surface area. McKewanl has given formal shape to this concept with mathematical derivation and has shown it to be valid for reduction of several iron ores, hematite, and magnetite, both by H2 and H2, H2O, N2 mixtures. Some other investigators, however, do not find this theory to be entirely valid. Deviations have been observed2 and further confirmedS3 Hansen4 also agrees that deviations do occur, at least in the latter stages of reduction, while from the data of several investigators summarized by Themelis and Gauvin,5 it is clear that the theory is not always applicable and further that, when it is applicable, it does not hold in the final stages of reduction. 3) Among those who claim the transportation of gas to be the rate-controlling step are Udy and Lorig,6 Bogdandy and Janke,7 and Kawasaki el a1.8 The validity of the theory has also been acknowledged indirectly by other research workers who show that the sintering and recrystallization of iron cause a decrease in reduction rate, for it is only if the transportation of gas is important that this sintering has any bearing. However, the theory has been rejected by some because they have failed to obtain

Jan 1, 1965

By Wm. Reuben Webster

Brass is an alloy of copper and zinc. The brass containing 70 per cent copper and brasses (using this term to denote all useful 30 per cent zinc. Fig. 3 shows the effect of proportions of the two constituents) are the annealing at various temperatures on the most valuable and widely employed of all same alloy. This effect is somewhat modi- nonferrous alloys, because of their high resistance to ordinary corrosive agencies and the very wide range of properties that may be imparted to them by variations in the proportions of the constituents and by variations in mechanical treatment and heat-treatment. Fig. I shows the normal physical properties, as determined by standard tensile tests, of the series when in the annealed condition. Fig. 2 shows the effect of varying amounts of cold-working on an almost pure fied by the degree of cold-working to which a brass has been subjected, as shown by Fig. 4. A fourth test, which is empirical, has been found useful because of its simplicity —the hot hammer test. Samples 1/2 in. in diameter and 3/4 in. long are placed in a suitable furnace. These are withdrawn one at a time. at successively higher temperatures and are subjected to the blow of a drop hammer weighing 50 lb. with a drop of 4 ft. The percentages of reduction in length of the cylinders are plotted against temperatures and give a camparative measure of plasticity at different temperatures. The results of this test on several

Jan 1, 1942

By Wm. Reuben Webster

Brass is an alloy of copper and zinc. The brass containing 70 per cent copper and brasses (using this term to denote all useful 30 per cent zinc. Fig. 3 shows the effect of proportions of the two constituents) are the annealing at various temperatures on the most valuable and widely employed of all same alloy. This effect is somewhat modi- nonferrous alloys, because of their high resistance to ordinary corrosive agencies and the very wide range of properties that may be imparted to them by variations in the proportions of the constituents and by variations in mechanical treatment and heat-treatment. Fig. I shows the normal physical properties, as determined by standard tensile tests, of the series when in the annealed condition. Fig. 2 shows the effect of varying amounts of cold-working on an almost pure fied by the degree of cold-working to which a brass has been subjected, as shown by Fig. 4. A fourth test, which is empirical, has been found useful because of its simplicity —the hot hammer test. Samples 1/2 in. in diameter and 3/4 in. long are placed in a suitable furnace. These are withdrawn one at a time. at successively higher temperatures and are subjected to the blow of a drop hammer weighing 50 lb. with a drop of 4 ft. The percentages of reduction in length of the cylinders are plotted against temperatures and give a camparative measure of plasticity at different temperatures. The results of this test on several

Jan 1, 1942

By Dennis Nottingham

Spin-fin pipe piles can develop large loads in tension, thus have evolved as a foundation product of great potential. Currently, over 500 spin-fin piles have been used successfully in dolphins, docks, buildings and bulkheads. Spin-fin piles are pipe piles with plates welded near the tip at a batter-in-screw fashion. Thus, as the pile is driven, the pile screws into position. Tests show this pile type to have highly unusual stress/strain relationships, wherein plunging failure is usually never reached either at normal or large deformations. Tension capacity can approach pile capacity in bearing; thus, large reserves are usually available for tension. Tests have been performed on 8-5/8-inch to 24-inch-diameter piles in silt, sand, and gravelly soil, to provide a broad spectrum of data.

Jan 1, 1990

By Alex Zapata, Miltón Carrión, Gustavo García

Pan American Silver Huaron ha decidido invertir U$S 4.3 millones en infraestructura de ventilación para la ejecución de chimeneas tipo Raise Boring que se ejecutarán en los diferentes circuitos de la mina, y que permitirán dar sostenibilidad al minado, profundizar las rampas hacia niveles inferiores y expandir los horizontes de la mina. Con los nuevos circuitos operando, la mina Huaron habrá reducido las resistencias de los circuitos de ventilación, por lo tanto, podrá trabajar posteriormente en controlar y reducir el consumo de energía por ventilación.

Sep 29, 2023

By W. A. Wood, H. M. Bendler

Cylindrical fatigue specimens of OFHC* copper were subjected to alternating torsion while under axial tension. The superimposed tension strongly influenced the fatigue life of the specimens as well as causing characteristic changes in the structure of the fissures that form and develop throughout the life of the specimen. A further effect of the superimposed tension is a continuous extension of the specimen throughout its life in a manner formally similar to creep at elevated temperatures. RECENTLY, studies of the structural changes leading to fracture of metals by fatigue have been made by a technique which reveals, in section, the lattice distortion arising from slip movements inside the metal and the disturbances built up by these slip movements at the metal surface.1'2 According to this approach, fatigue develops as follows: a) fine slip movements concentrate in bands, producing little strain-hardening and thus permitting abnormal totals of plastic strain before fracture and, therefore, abnormal amounts of lattice distortion along each slip band; b) both forward and backward slip movements occur in each band which, according to their distribution across the band, may build up surface disturbances that include sharp notches; c) these notches early in the life of a specimen penetrate the distorted slip zones and transform them into deep, fine fissures; d) the fissures on continued cycling locally saturate the metal and cause local collapse in the form of a microcrack. Thus, the significant consequence of fatigue or cyclic

Jan 1, 1962

By J. Egan

The recovery of gold by ore leaching is influenced by the size of the particles and the chemical environment. Within the experimental error associated to the testing of gold ore, results of a series of leaching tests conducted with natural ores rather than monosized samples confirm that gold dissolution increases with decreasing ore particle size. The tests also indicate that the dissolution of gold in the ore within a size interval is weakly affected by the intensity of the size reduction method.

Feb 27, 2013

By T. J. Carew

The application of many standard estimation techniques to deposits with a significant degree of folding or faulting can be difficult, mainly because of the necessity to maintain the correct spatial relationship between the samples and the points being estimated. Various transformations must be applied to the points of interest before variography and estimation can be applied, followed by back transformation into the original space. This paper presents an unfolding technique developed by Gemcom Software International that minimizes the inherent distortion in the process and also provides an example of the technique in folded and faulted situations.

Jan 1, 2002

By Harrison R. Cooper

Composition data is needed as input for executing process control and management of particulate separation for flotation control. While requirements for composition data can be satisfied in many cases by manual sampling and analysis, automatic sampling and assay systems are now viewed as justified for all but the simplest or smallest processes. On-stream X-ray fluorescence analysis (XRFA) has satisfied requirements for the main portion of metalliferous sulfide ore flotation processes as XRFA technology evolved in reliability and sophistication from its beginnings in the late 1950's. In recent years, advanced on-stream analysis technologies have reached levels of development suitable for use in process control to increase efficiencies of important processes in mining and minerals industries such as coal fines flotation and industrial minerals beneficiation (particularly phosphate beneficiation) where XRFA methods have been inapplicable. Recent technical developments pertinent to use of advanced technologies as well as improvements to established on-stream composition analysis methods are discussed.

Jan 1, 1989

By M. S. Celik

Adsorption of sodium dodecylsulfonate (SDS) and dodecylaminium hydrochloride (DAH) on Buller seam coal, New Zealand, have been studied. Both surfactants adsorb effectively on the coal below pH 8, and the adsorption isotherms established at pH 4 are essentially the same at lower concentrations. These findings suggest that the adsorption of these two ionic surfactants on coal is controlled by a hydrophobic bonding mechanism. However, the results of calorimetric studies suggest that coulombic attraction also plays a part in the adsorption mechanisms. It has also been found that both the SDS and DAH adsorbed in the first monolayer are not removed by lowering the surfactant concentrations in the bulk solution.

Jan 1, 1993

By G. Thodos, W. F. Stevens

The point-source function introduced by Horner' us a solution to the general unsteady-state equation for the flow of fluids through porous media has been utilized to calculate pressure profiles for adjacent wells as a function of time. By trial and error, the time at which the pressure waves meet to cause interference can then be calculated. For this calculation, the time of interference is arbitrarily defined as that time when both pressure waves exhibit a pressure decrease of 25 psi ar the same point within the formation. To illustrate the method, an example involving two adjacent wells producing at different rates has been worked out and is presented in detail. INTRODUCTION The initiation of production of a new well is usually accompanied by pressure drawdown measurements in order to establish the extent and characteristics of the formation. The interpretation of such pressure drawdown data is based on mathematical developments involving a single well in an infinite reservoir. If more than one well is present in a reservoir, the possibility of interaction between wells exists. Therefore, care must be taken in interpreting the pressure drawdown data. It becomes important to be able to determine when this interaction, or interference, becomes significant. This paper presents a method for the prediction of the approximate time of interference between two such adjacent wells. The basic differential equation describing the pressure distribution existing during unsteady-state flow of a slightly compressible fluid has been solved by Hor-ner.' for a constant production rate from a circular homogeneous reservoir of infinite extent. The solution utilizes the point-source function to define the pressure at various points within the formation as a function of time. The resulting expression is: q = production rate, STB/D ,;= formation volume factor, dimension-less µ = fluid viscosity, cp k = formation permeability. md H = formation thickness, ft C - fluid compressibility, psi' F = formation porosity, dimensionless R = distance from centerline of well, ft T = production time, hours Ei(—u) = Ei-function of U Eq. 1 may be used to calculate the pressure profiles generated during production from a single well in an infinite reservoir.