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By M. Hansen, C. C. Wang

THE 6 phase of the Cu-Sn system (Cu,Sn, = 32.53 pct Sn) was considered to be stable down to room temperature until Owen and Iball showed by X-ray analysis that it undergoes a eutectoid decomposition into the a and e phases at a temperature near 300°C. Their findings have been confirmed by other investigators,2-5 a11 of whom used X-ray diffraction studies of powdered specimens. The transformation temperature has been reported by various authors as lying between 300" and 380°C. To our knowledge, no microscopic evidence of the eutectoid reaction has been published, as yet. It was in connection with other work that longtime annealings at 300°C were conducted with alloys containing 22, 32.6, and 35 pct Sn (nominal compositions) prepared from electrolytic copper and electrolytic tin and cast in a small iron mold. The specimens were first annealed at 700°C for 5½ hr and quenched from 400 °C after cooling to, and annealing at, that temperature for 9½ hr. After this treatment the sample with 22 pct Sn was cold worked for 15 pct reduction in thickness; the 32.6 and 35 pct alloys were too brittle to be cold worked. The final anneal at 300°C was done in a sealed pyrex glass bulb for 63 days. Fig. 1 represents the microstructure of the annealed alloy with 22 pct Sn. It shows primary a solid-solution crystals in a matrix of the (a + 8)-eutectoid formed at 520 °C. The a crystals contain 8 inclusions which precipitated from a due to the decrease in the solubility of tin in copper with fall in temperature. The decomposition of the 8 phase into a (light) and E (dark) can clearly be seen in some areas of the (a + 8)-eutectoid matrix. However, the decomposition is far from being completed, even after the long-time anneal used. Figs. 2 and 3 depict the microstructures of the annealed 32.6 pct alloy, which was intended to consist entirely of 6 phase. Due to some loss in copper on melting, the composition is slightly higher in tin. Accordingly, the sample after quenching from 400 "C consisted of grains of the 8 phase with the e phase arranged along the grain boundaries and as a Wid-manstatten precipitate within the 6 grains. After an annealing time of 63 days, the eutectoid decomposition, 6 + a + e, is still in its early, initial state. The pearlitic type of eutectoid is nucleated at the c crystals, preferably those surrounding the grain boundaries of the 8 phase. The appearance of the (a + €)-eutectoid in the 35 pct Sn alloy was very similar to that shown in Figs. 2 and 3. Again, the eutectoid decomposition nucleated at the 6 phase and proceeded from there into the 8 areas. As is evident from Fig. 2, the rate of decomposition of the 6 phase at 300°C is extremely sluggish: In the representative area shown only about 5 pct of the 8 phase has undergone the eutectoid trans- formation after annealing for 63 days. On the other hand, Owen and Williams2 have reported that X-ray photographs of powdered samples with between 17.5 and 34 pct Sn did not show 8 lines after annealing for only five to seven days at 300°C. This is in accordance with the fact that the rate of reaction in powdered samples is higher than in massive specimens, as a result of the excess free energy of the powder (due to its greater surface area). The authors wish to express their thanks to C. A. Johnson for preparation of the micrographs.

Jan 1, 1952

By W. H. Eardley

It is increasingly evident that the excellence of blast-furnace operation to a great extent depends upon the preparation of the products fed into the furnace. The preparation of these products is carried on largely in the roasting and sintering departments. Prior to the building of flotation plants in Utah and other western states for the treatment of lead-zinc ores, the gravity concentrates received at the Midvale smelter amounted to about 4000 tons per month, containing 24 per cent. lead and 10 or 11 per cent. zinc. This product was about 20 mesh—that is, 45 per cent. of it would be plus 20 mesh and the balance minus 20 mesh. About 1000 tons of pyrite per month, containing 5 per cent. lead and 10 per cent. zinc, was also received. These products were sent to the multiple-hearth roasters for calcining, after which they were sent to the Dwight-Lloyd machines for sintering with other ores. The sintering charge passed over the machines but once. The first flotation products received consisted of a wet, sticky, muddy mass, containing a large amount of moisture, up to 19 or 20 per cent., and it was almost impossible to feed them with any degree of regularity, if at all, through our standard feeders; but the amount of flotation product received during the first year or so was relatively small and it virtually lost its identity by being mixed with a large amount of jig and table concentrates. As the quantity of flotation products increased, more efficient filtering was accomplished and the moisture greatly reduced. Flotation Products Received At the present time the Midvale plant receives about 4300 tons per month of flotation product running 60 per cent, lead and 4.5 per cent. zinc, 85 per cent. of which is minus 200 mesh and contains about 8 per cent, moisture; and 4000 tons per month of pyrite of similar fineness, running about 2 per cent. lead and 3.5 per cent. zinc, containing about 10 per cent, moisture. The lower moisture greatly reduces the difficulties of handling, making it possible to run a 100 per cent. flotation feed on a multiple-hearth furnace without serious mechanical troubles. The calcine, however, would contain nodules and balls of unroast,ed concentrates, sulfur elimination

Jan 1, 1928

By W. H. Eardley

IT IS increasingly evident that the excellence of blast-furnace operation to a great extent depends upon the preparation of the products fed into the furnace. The preparation of these products is carried on largely in the roasting and sintering departments. Prior to the building of flotation plants in Utah and other western states for the treatment of lead-zinc ores, the gravity concentrates received at the Midvale smelter amounted to about 4000 tons per month, containing 24 per cent. lead and 10 or 11 per cent. zinc. This product was about 20 mesh-that is, 45 per cent. of it would be plus 20 mesh and the balance minus 20 mesh. About 1000 tons of pyrite per month, containing 5 per cent. lead and 10 per cent. zinc, was also received. These products were sent to the multiple-hearth roasters for calcining, after which they were sent to the Dwight-Lloyd machines for sintering with other ores. The sintering charge passed over the machines but once. The first flotation products received consisted of a wet, sticky, muddy mass, containing a large amount of moisture, up to 19 or 20 per cent., and it was almost impossible to feed .them with any degree of regularity, if at all, through our standard feeders; but the amount of flotation product received during the first year or so was relatively small and it virtually lost its identity by being mixed with a large amount of jig and table concentrates. As the quantity of flotation products increased, more efficient filtering was accomplished and the moisture greatly reduced. FLOTATION PRODUCTS RECEIVED At the present time the Midvale plant receives about 4300 tons per month of flotation product running 60 per cent. lead and 4.5 per cent. zinc, 85 per cent. of which is minus 200 mesh and contains about 8 per cent. moisture; and 4000 tons per month of pyrite of similar fineness, running about 2 per cent. lead and 3.5 per cent. zinc, containing about 10 per cent. moisture. The lower moisture greatly reduces the difficulties of handling, making it possible to run a 100 per cent. flotation feed on a multiple-hearth furnace without serious mechanical troubles. The calcine, however, would contain-nodules and balls of unroasted concentrates, sulfur elimination

Jan 1, 1928

By Paul W. Chase

Centralized process control has received increasing emphasis in recent years. Its application at U. S. Steel's Minntac facility for production of taconite pellets is discussed in this paper. A brief description of the flowsheet will provide background for discussion of the process instrumentation and digital system.

Jan 1, 1969

By A. B. Parsons

When the Seeley W. Mudd Memorial Fund was established in. 1929 the donors mentioned certain types of projects to which preference might be given in selecting those to he financed by the income from the Fund. One suggestion. was that the projects "be of particular benefit to young engineers." This modest little book meets this specification most aptly. It seeks to guide the engineer-particularly the young one-with the least loss of time and effort to the most convenient source of authentic information regarding any topic in which he may at the moment be interested. Knowing the best place to find the literature on a subject is almost as valuable-and far more practicable-than maintaining a library of one's own large enough to provide the information.

Jan 1, 1933

By C. Gregory Knight

The Pennsylvania Coal Model is a research activity of the College of Earth and Mineral Sciences of the Pennsylvania State University, in association with the Economic Development Council of Northeastern Pennsylvania, and the Southwestern Pennsylvania Regional Planning Commission. In this project, sponsored by the Appalachian Regional Commission and the Pennsylvania Science and Engineering Foundation, data banks and models have been developed to simulate potential coal production and utilization systems in Pennsylvania. Building from a coal system data base for 1974 and mining simulation models, computer optimization models predict potential coal production and transportation for alternative future demand scenarios. The model allows derivation of costs of various coal supply systems under specific economic, transportation, and environmental constraints. The model also provides insight into such impacts of coal production as employment, land use, and environmental quality.

Jan 1, 1977

By R. C. Mahon

Operators concerned with the destruction of their piping by acid mine waters will be interested in the method by which this problem was solved at the Cardiff mine of the Homer group. Rubber lined, or acid resisting metal pipes were found too expensive. Casting concrete lining in pipe would have required a minimum thickness of one inch, thus excessively reducing the pipe's diameter, as well as taking twenty four hours per length of pipe. The Naylor Pipe Co. of Chicago, having experimented with centrifugal lining of pipe with concrete, provided information which eventually solved the problem. An experimental plant was constructed as shown, and the following procedure developed : (1) Kerosene is used to remove the interior oil coating of new pipe. Closed with blank flanges, the pipe is revolved for eight minutes at varying speeds. Stopping and starting the motor achieves a good washing action. The kerosene is then drained off, and similar washing action with caustic soda removes any excess. Swabbing in done with burlap fastened to a 1/2-in. pipe. (2) The aggregate, made of one. part quick-setting cement and two

Jan 1, 1949

By R. V. Higgins, A. J. Leighton

Interest by petroleum engineers in the flow of three phases—oil, gas and water—in irregularly bounded porous media lies mostly in the performance calculation of water floods of reservoirs that have been partially depleted as the result of expansion of much of the originally dissolved gas. The authors present a method to forecast three-phase flow in complex geometry and explain the details by the use of a specific example of a five-spot water flood of a partially depleted stratified reservoir. In this example, the fluid and rock properties of a field given by Prats, et al,' were used. The computed results fit the field performance more accurately than Prats, et al, and Slider.' The time required for the high-speed digital computer to make the calculations, including the contributions from the different layered zones, is about one minute. INTRODUCTION The declining rate of discoveries of new oil fields in the United States makes the recovery of more oil from known reservoirs more attractive than previously. Water flooding has an excellent proved background for recovering additional oil economically. Accordingly, the main interest of this paper is in this type of recovery. In petroleum engineering studies, commercial interest in three-phase flow is mostly in the water flooding of reservoirs in which the oil has been partially produced by the expansion of dissolved gas. When water is pumped into these reservoirs, three-phase flow takes place. Although this paper is concerned with these conditions, the principles involved could be used for other conditions when and where they come to the fore. Many investigators have made contributions to non-empirical forecast methods using basic scientific engineering principles. Several of these used the oil in place at the start of the water flood and the oil remaining after a large quantity of water has passed through a core for key values in their calculations. Recently, Prats, et al,' and Slider have reduced assumptions by adding the third phase—gas—in their forecasting methods. Slider uses the mobilities in the immediate vicinity of inlet and outlet wells as an aid to simulate the resistance effect in the five-spat pattern of the flow of oil, gas and water. Prats, et al. minimize assumptions by using previously determined laboratory data for determining sweep efficiency in the five-spot pattern. In neither of these papers is the saturation profile continuously affected by permeability-saturation curves. Sheldon and Dougherty- recently described a method that employs continuously changing saturation profiles using permeability curves, has a minimum of assumptions and needs no prior sweep efficiency. The Higgins-Leighton method, described in this paper, has all of these features; however, many of the techniques are different from those of Sheldon and Dougherty. The Higgins-Leighton method, tested in May, 1961, is direct and easy to apply and requires very little computer time to calculate a forecast. The short computer time is especially helpful in the study of a reservoir containing many layers of different relative permeabilities. In the Higgins-Leighton method, the individual pressures do not have to be calculated, as the resistance to flow in each cell in the flow pattern is readily determined without the use of any iterative techniques. The saturation and permeability distributions are readily determined. These data and the shape factor, which is measured only once from the potentiometric model when mobility ratio is one, determine the resistance to flow in each cell. THEORY The authors showed in a previous paper4 that, as an aid to calculating performance, the reservoir can be divided into channels using the streamlines of a potentiometric model as a guide. See Fig. 1. This procedure also was used in this paper. The authors also showed that, by treating conduits as approximately one-dimensional and neglecting pressure gradients transverse to the main flow, the Buckley-Leverett equation may be expressed as The principles expressed by this equation are employed extensively in the three-phase flow, as they were in two-phase flow. In the three-phase flow, the channels (the size and shape of which are taken from a potentiometric model)

By AIME AIME

MODERN metallurgy is an art and a science. The art is process metallurgy-extracting metals from their ores, refining them, and alloying them with one another and with certain nonmetals to produce thereby a variety of metallic materials which, owing to a wide range of useful properties, are for many purposes more valuable to man than the individual metals themselves; process metallurgy also includes shaping or otherwise treating metals and alloys to form objects useful to a complex industrial world. The science is physical metallurgy-organized knowledge of the constitution and internal structure of metals and alloys, of the relation of their composition and structure to properties, and of the laws, theories, and hypotheses that purport to explain this relation.

Jan 1, 1942

By L. F. Mondolfo, B. E. Sundquist

The undercooling associated with the nucleation of the secondary phase from the liquid by the solid primary phase was studied in sixty binary alloys by means of a hot-stage microscope. It was found that in a system of a and ß, a usually nucleates ß at low undercoolings, but ß does not nucleate a, except possibly at undercoolings approaching homogeneous nucleation. This behavior can be explained in terms of relative interfacial energies and shows that crystallographic disregistry is only a minor factor in heterogeneous nucleation from metallic liquids. PREVIOUS experimental work1-6 on nucleation of solids from liquids has shown that normally nucleation is heterogeneous, and that small solid particles present in the liquid are responsible for the nucleation. These experiments and the theory that has evolved from them have made apparent that there is a "characteristic undercooling" associated with the nucleation of the solid from a given liquid by a given impurity. Little is known, however, about the chemical and structural relationships between the nucleating agent and nucleated solid that control the effectiveness of the nucleating agent in catalyzing the nucleation, as measured by the required undercooling. A review of the literature has yielded seventeen undercoolingsL-6 for the nucleation of solid from liquid metals by "known" nucleating agents. All values come from experiments in which the metal studied was divided into a number of particles (10 to 300 pin diam.) much larger than the number of extraneous impurity particles so as to obtain a large number of particles free of foreign nucleating catalysts. Known nucleating agents are then introduced by coating the droplets with particles or a thin film of the catalyst. Six of the seventeen undercooling values referred to cases where, for various reasons, the identity of the nucleating species was not at all certain. Another six cases involved nucleating agents with a crystal structure that was not known. Four other cases involved undercoolings listed as greater than or equal to undercoolings which were very likely those for homogeneous nucleation. One investigation3 involved adding to droplets powdered oxides, carbides, and so forth that were doubtlessly covered with adsorbed oxide or nitride films. The highly variable nature of these films resulted in highly variable undercooling (as was also found in preliminary work in this investigation). It is apparent that the information on heterogeneous nucleation in liquid metals is too limited to give rise to any definite conclusions on the nature of the catalytic process. With these problems in mind a new method was

Jan 1, 1962

By Walter W. Lilly, Issa S. Oweis

Application of rock engineering in geotechnial consulting practice considered herein is in areas of: (a) bedrock verification for foundation support, (b) bearing capacity and settlements, and (c) excavations. A routine geotechnical investigation usually provides data on depth to rock, rock classification, and rock quality. In cases of rock outcrop, such outcrops are mapped for geologic structures and rock mass description. In addition, the regional geology and the general aspects of the groundwater regime are usually known from either published literature or previous experience. The predominant technique for ground and site investigation are usually drilling and geologic reconnaissance. Other techniques involving seismic and geophysical soundings, borehole camera, and oriented cores are used by by no means routine. Performing laboratory strength and compressibility tests is often made to be considered as routine. The use of the point load test is gaining increasing use in the United States and would, perhaps, become a routine field or laboratory test due to its simplicity and, more importantly, its relatively low cost. The purpose of this paper is to describe cases where mostly routine investigation and testing were used to arrive at engineering decisions. Bearing Capacity and Settlements The allowable bearing values for foundation support on rock is usually dictated by local building codes which presumably should reflect local experience. The interpretation of the code, however, can present a problem, especially if the interpretation is made by a designer under the delusion of knowledge in rock engineering. For

Jan 1, 1982

By C. H. Stein

The Pennsylvania Legislature, on March 13, 1837, passed an act authorizing the Lehigh Coal & Navigation Co. to construct a railway to connect the North Branch Division of the Pennsylvania Canal with the slack water navigation of the Lehigh River; the navigation company accepted this act on May 10, 1837. Edwin A. Douglas, chief engineer for the navigation company, located the route for this railway from White Haven to Wilkes-Barre, which was called the Lehigh & Susquehanna Railroad. The object was to transport coal from the Wyoming Valley, of Pennsylvania, to the Atlantic seaboard. This railway was considered a marvelous piece of engineering, as it included a tunnel nearly 55 mi. long, and a series of inclines, or planes, up which the cars laden with coal were raised from the vicinity of Ashley to the summit of the mountain near Solomon's Gap, whence they were taken to White Haven by rail. There the coal was transferred to canal boats. In June, 1862, floods almost completely destroyed the upper division of the canal, so on March 4, 1863, the Pennsylvania Legislature passed an act prohibiting its restoration, but granted a charter for the construction of a railway from White Haven to Mauch Chunk to connect with the line from White Haven to Wilkes-Barre, previously built. On March 16, 1864, a supplementary act was passed extending the Lehigh & Susquehanna Railroad to Easton, Pa. This completed a direct all-rail route from Wilkes-Barre to the New York harbor (by way of the Central Railroad of New Jersey). Up to this time, all freight and passenger traffic passed over the planes, but in 1866 and 1867 there was constructed what was known as the "back track" down the mountain side between Solomon's Gap and Ashley over which all the passenger traffic and empty cars thereafter passed; it is now known as part of the main line. For the handling of the heavy coal traffic, however, this would have involved a continuous climb from Ashley, 170.27 mi., from New York, to Solomon's Gap, 157.8 mi. from New York, or a distance of 12.47 mi., and a total ascent of 1013.75 ft., composed of grades 95.61, 83, and 51.4 ft. per mi., respectively, and

Jan 1, 1922

David T. Day, Washington, D. C.: The paper of Mr. Adams is chiefly valuable because it emphasizes the ease with which petroleum can migrate in the earth's crust. Concerning this migration, I have little faith in the rôle of water as a carrier of gaseous or liquid hydrocarbon, suspended or mixed in the water in any way. My lack of faith is due to observation of

Jan 1, 1903

ALBERT Ladd Colby, who died suddenly of influenza at Torquay, England, on Apr. 30,1924, was born in New York City, on June 26,1860. He was educated in the public schools of New York, at the College of the City of New York, and received the degree of Ph. B. from the Columbia School of Mines in 1881. He continued his studies at Columbia, acting occasionally as assistant to Prof. C. F. Chandler, until 1883. For the next three years he was Assistant Professor of Chemistry in Lehigh University; then head chemist and metallurgical engineer of the Bethlehem Steel Co., at Bethlehem, Pa., occupying the latter position until 1903. As head chemist his active and inventive mind devised several improvements in apparatus for increasing the rapidity and accuracy of the analytical work; as metallurgical engineer, he was, from time to time, in charge of the blast-furnace, open-hearth, bessemer, and puddling departments; he had entire charge of the inspection, assignment, and economic use of all metallurgical materials, and he early gave his attention to the formulation of specifications for metallurgical materials—an activity in which he long held a distinguished part in this country, and as a representative of his own country in England and Europe. He also sewed as expert for his company in patent suits, again laying the foundation for valuable service later as a consulting engineer. In this latter capacity he was excelled by few, if any, contemporaries in the iron and steel industry. His mind was ingenious, thorough, clear, and keen, both in the preparation of evidence and its presentation to the Court. He very quickly appraised the value of evidence, or of an answer to a question, and knew how to secure the infermation, either from the available literature of any language, or by special researches or plant studies. In the executive control of literary research for patent purposes, his long training, infinite capacity for digging through long series of articles in English, German or French, and clear formulation of the vital subject matter for the guidance of assistants, made him invaluable. He was also an adept in collecting information on special branches of his profession. For example, when the science of metallography began to assume importance, he made the first really comprehensive bibliography covering the literature of all siderurgical countries; for the newly formed International Nickel Co. he gathered all the information extant on the subject of nickel steel, both in the literature and in the minds of experts in America and Europe. Two books testify to the thoroughness of his work in this capacity, vie.: "American Standard Specifications for Steel,"

Jan 1, 1924

By Jay A. Carpenter

THIS preliminary report from the Committee to Study Relations Between Students and the Institute is submitted to our member- ship for consideration and discussion before the general subject comes up for action at the Annual Meeting in February. At present, the A. I. M. E. has a dual relationship with mining students, each relationship in no may connected with the other. To the individual student the Institute offers for $2 a year a Student Associateship in the Institute which carries with it a subscription to MINING AND METAL- 'LURGY, a watch fob, and the privilege of becoming a Junior Member after graduation without payment of the -first year's dues, if one's application is accepted. To the student's college society it offers the privilege, upon application, of becoming 'an Affiliated 'Society, which brings with it no specific supervision or aid, and in turn requires no specific conditions as to membership, fees, or rules. This Affiliated Society is distinctly a school organization which Student Associateship in the Institute can he given special status or ignored, is the local .society sees fit.

Jan 1, 1934

By A. Romero-Juarez

This paper is concerned with the effect of propping-agent concentration on flow capacity of a fracture in the case in which there is embedment of the propping agent. Previous published studies have shown definitely that there is a relationship between fracture flow capacity and prop ping-agent concentration, and it has been shown that the theoretical results are confirmed by laboratory experiments. The problem of directly finding sand concentration for maximum flow capacity of a sand-propped fracture is solved, and formulas and charts are given to obtain this concentration under various conditions of effective overburden pressure, medium sand-grain diameter and rock properties. It is shown that, for the same effective overburden pressure and the same rock characteristics, optimum sand concentration in pounds per gallon does not depend on medium sand diameter. For conditions met in bydraulic fracturing operations, it is found that sand concentration in grains per square inch for maximum flow capacity varies within a wide range of values; this indicates the convenience of using data of fracturing pressure and rock characteristics for calculating sand concentration in order to achieve the best results in fracture treatments. INTRODUCTION It has been pointed out in the published literature1 that one important factor controls the success of a hydraulic fracturing operation — the propping of the fracture. The main effect of the propping agent is to hold the fracture open by means of the reaction forces that oppose the pressure due to the overburden. It is assumed in this paper that the propping agent is sand, that the grains are spherical and uniform in size, and that this sand is distributed in a monolayer in the fracture. The existence of a sand concentration value for maximum fracture flow capacity has been recognized since the publication of one of the first studies on the subject.2 In the reference cited, flow capacity was assumed to be proportional to the cube of the fracture volume per square inch not filled by sand. The obtained experimental curves relating to flow capacity and sand concentration had the same appearance as the curves obtained with the afore-mentioned assumption. Recent work3 has shown that fracture permeability, in the case of a monolayer, can be calculated accurately by means of a modified Kozeny-Cacman equation; thus, it can be shown that fracture pqmeability is a function of free volume in the fracture and of the rock and sand wet surfaces. The flow capacity of a fracture is dependent on the permeability of the fracture and on the fracture width. If all excessive quantity of sand is present in the fracture, its width may be large but its permeability i:; low due to the greater flow resistance; too few grains of sand per square inch are present in the fracture, sand embedment in the rock is greater and the width becomes small enough to appreciably decrease the rate of flow. To determine optimum conditions of flow, therefore, it is necessary to know the dependence of fracture width on density or concentration of propping agent. This relation is given in a study4 in which the approach to embedment is similar to the one made in a penetration hardness test of metal. With the equacions presented by Darin and Huitt,3 the number of sand grains per square inch that results in maxirnum fracture capacity can be determined graphically by plotting fracture capacity vs sand concentration. Since the relationship between fracture capacity and sand concentration may be considered known, one is led to formulate the analytical problem of directly determining sand concentration for maximum fracture flow capacity, in order to study the effect of the various quantities that come into the process. The solution of this problem appears to be interesting both from the viewpoint of fluid mechanics and from the practical viewpoint of oil production in hydraulic fracturing treatments. EQUATION FOR FRACTURE FLOW CAPACITY It can be shown3 that the fracture flow capacity of a monolayer is given by the following expression,

By John J. Van den Broek

As the established tailings disposal techniques do not meet the requirements of today, alternative methods of disposal are explored. McIntyre Mines Ltd., Coal Div. found a solution in the construction and operation of a tailings dewatering plant. The solids are recovered from the tailings slurry by means of mechanical dewatering equipment and are then dried in a unique drying system to provide an excellent thermal fuel for a power generating station.

Jan 1, 1983

By D. Havlena, A. S. Odeh

The material balance equation used by reservoir engineers is arranged algebraically, resulting in an equation of a straight line. The straight line method of analysis imposes an additional necessary condition that a successful solution of the material balance equatiott should meet. In addition, this algebraic arrangement attaches a dynamic ineuning to the otherwise static material balance equation. The straight line method requires the plotting of one variable group vs mother variable group. The sequence of the plotted points as well as the general shape of the resulting plot is of utmost importance. Therefore, one cannot progrm the method entirely on a digital computer ar is usually done in the routine solution of the material balance equation. If this method is applied, then plotting and anaIysis are asential. Only the appropriate equations and the method of analysis and interpremtion with comments and discussion are presented in this paper. Illustrative field examples for the various cases treated are deferred to a subsequent writing. INTRODUCTION One of the fundamental principles utilized in engineering work is the law of conservation of matter. The application of this principle to hydrocarbon reservoirs for the purpose of quantitative deductions and prediction is termed "the material balance method of reservoir analysis". While the construction of the material balance equation (MBE) and the computations that go with its application are not difficult tasks, the criteria that a successful solution of the MBE should fulfill have always been a problem facing the reservoir engineer. True and complete criteria should embody necessary and dcient conditions. The criteria which the reservoir engineer uses possess a few necessary but no sufficient conditions. Because of this, the answers obtained from the MBB are always open to question. However, the degree of their acceptability should increase with the increase in the number of the necessary conditions that they should satisfy. Generally, the necessary conditions commonly used are (1) an unspecified consistency of the results and (2) the agreement between the MBE results and those determined volumetrically. This second criterion is usually overemphasized. Actually, the volumetrically determined results are based on geological and petrophysical data of unknown accuracy. In addition, the oil-in-place obtained by the MBE is that oil which contributes to the pressure-production history,' while the volumetrically calculated oil-in-place refers to the total oil, part of which may not contribute to said history. Because of this difference, the disagreement between the two answers might be of paramount importance, and the concordance between them should not be overemphasized as the measure of correctness of either one. In this paper, a third necessary condition of mathematical as well as physical significance is discussed. It is not subject to any geological or petrophysical interpretation, and as such, it is probably the most important necessary condition. It consists essentially of rearranging the MBE to result in an equation of a straight line. This straight line method of the MBE solution has invalidated a few long time accepted concepts. For instance, it has always been advocated that if a water drive exists, but one neglects to take it into account in the MBE, the calculated oil-in-place should increase with time. The straight line method shows that in some cases, depending on the size of the neglected aquifer, the calculated oil-in-place might decrease with time. The straight line method requires the plotting of a variable group vs another variable group, with the variable group selection depending on the mechanism of production under which the reservoir is producing. The most important aspect of this method of solution is that it attaches a significance to the sequence of the plotted points, the direction in which they plot, and to the shape of the resulting plot. Thus, a dynamic meaning has been introduced into the picture in arriving at the final answer. Since the emphasis of this method is placed on the interpretation of the sequence of the points and the shape of the plot, one cannot completely automate the whole sequence to obtain "the best value" as normally done in the routine application of the MBE. If one uses the straight line method, then plotting and analysis are musts. The straight line method was first recognized by van Everdingen, et al,2 but for some reason it was never fully exploited. The advantages and the elegance of this method can be more appreciated after a few cases are carefully treated and worked out by it. SOLUTION OF THE MATERIAL BALANCE EQUATION SATURATED RESERVOIRS The MBE for saturated reservoirs written in AIME symbols is

By J. D. Corbett

Mining geophysics in 1967 continued to expand with greater application in the exploration and development of mineral deposits. Moreover, geophysical activity increased without the particular emphasis of a Pine Point or Timmins discovery to spur interest. This trend is expected to continue through 1968 as geophysics more and more becomes an integral part of a mineral exploration program. This past year saw the "little black box" of the old-fashioned "doodlebugger" pushed further into the background, replaced by increasingly sensitive equipment of sophisticated design. The trend also is away from the one man geophysical operation wherein the same individual is responsible for the development, design and operation of the field gear, the planning and execution of a survey and analyzing and interpreting the data. In today's technology a staff of specialists, electronics engineers, mathematicians, physicists-to name but a few- are required to back up the exploration geophysicist in the development of new methods and techniques, in the reduction of the voluminous amount of field data and in the interpretation of the anomalies which can be enhanced by various high-speed computer techniques. Obviously a full back-up staff of these varied abilities is impractical to most exploration companies. However, the equivalent function is provided to the lone staff geophysicist by the many competent geophysical contractors and individual consultants.

Jan 2, 1968

By C. F. Riisness, E. R. Parker

THAT grain size has a great effect on the mechanical properties of metals has been recognized for a long time. Bassett and Davis1 in 1919 did excellent work in [ ] determining the effect of grain size on the hardness of brass. About the same time Jeffries2 and Sykes3 ascertained the effect of grain size on the strength and ductility of several metals at temperatures ranging from 80°K. to their melting points. When creep was recognized as an important property of metals, those engaged in the study of this property tried to determine the effect of grain size 4-9 on creep rates. Unfortunately, most of the investigations were conducted on only two grain sizes, often designated simply as "fine" and "coarse." It is well known that at high temperatures coarse-grained test bars creep less than fine-grained bars. The relation between grain size and size of test bar, [ ] however, has been frequently overlooked. In his early work, Jeffries2 showed that the number of grains in the cross section has a more important influence on the properties of the material than the actual grain size. More recently Hanson and Sandford10 and Pell-Walpole,11 in their measurements of the creep and tensile properties of tin, tested a wide range of grain sizes and correlated the grain size with the strength. Hanson9 later established the relation between the number of grains in the cross section and the. creep rate: At high temperatures, generally a coarse-grained structure is considered superior in creep to a fine-grained structure, but it is evident that for a given bar size continuously increasing the grain size will

Jan 1, 1944