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By Charles T. Baroch, Corbin Allardice

Nuclear energy probably has greater potentialities for changing the world's way of life than any other recent discovery. The atomic-bomb bursts over Hiroshima and Nagasaki suddenly changed the concepts of war. Peaceful uses of nuclear energy are advancing so rapidly that no study of economic trends is complete without giving them consideration. The minerals specialist, especially, must be aware of this new force in our lives, as minerals and metals are essential in harnessing the new force, and atomic energy itself is rapidly improving its competitive position in the energy field. Future historians may chronicle December 2, 1942, as the beginning of the Atomic Age. On that day Enrico Fermi and his co-workers at the University of Chicago produced and controlled the first self-sustaining nu- clear chain reaction. Like many inventions, the first application of nuclear energy was as a weapon of war. However, its potential usefulness in man's work and welfare far outweighs in economic importance its destructive use in war, unless its military effect would be considered so great and all-embracing that no major power will hereafter chance a world conflict. Recognition of this potential has generated a vast international effort to exploit the atom for peaceful beneficent purposes. Like its physical manifestation, the advent of nuclear energy has unleashed chain reactions that have pervaded the political, social, and economic environments of the world. The impact of nuclear developments in one of many fields is exemplified by the uranium mining industry. Uranium was discovered in 1789 and in the next century and a half it found only an insignificant use as a ceramic coloring agent; in fact, in the latter part of that period, it was a largely unsalable by-product of the radium and vanadium industries. Up to 1940 the total quantity of uranium metal produced was not more than a few grams, of doubtful purity. Thus the production of 12,400 pounds of pure

Jan 1, 1959

By R. W. Kraft

A back- reflection precession-type X-yay camera for determining the crystallographic orientation of the crystallites of both phases in small areas of thick specimens of polyphase alloys is described ad the geometry, advantages, and limitations of the apparatus are discussed. Metallographic obseg-vations of interfacial angles (or habit planes or growth direction are made on the same specimen so that the crystallographic and metallographzc orientation data call be directly correlated. An example of the application of tile technique to a unidi-~~ectionally solidified CuA12-A1 eutectic specimen is presented. The interfacial planes ad growth directions of each phase were established, and the orientation relationship between the phases was observed and found to be approximately intermediate between two previously reported relationships. The crystallographic interfacial relationship between two solid phases is an important parameter in a variety of metallurgical phenomena because of the energy associated with the interface and because this energy is at least partly associated with the way in which the two space lattices are in contact along the interface. In order to describe the interfacial planes in the crystallites of both phases it is necessary to determine the crystallographic orientation of each phase in a specimen relative to each other, and to directly correlate these data with met-allographic measurements from which the interfacial planes can be determined on the same specimen. The back-reflection Laue technique is the easiest way to determine the orientation of thick single crystals or large grains and the method can be combined with metallographic techniques to provide the necessary data, provided the reflections from each phase can be distinguished from one another. However, if the crystallites are small or of varying orientation or if one or both phases has a unit cell with less than the maximum symmetry, many overlapping and complex Laue patterns are recorded simultaneously and it becomes impractical if not impossible to interpret the photographs. All of these complexities were present in a unidirectionally so- lidified A1-CuA12 eutectic alloy1 for which a crystallographic analysis was desired. Consequently the method described here was developed since no known X-ray or electron diffraction technique had all of the following attributes which were required. 1) Method should yield data from which the crys-tallographic orientation of every crystallite or diffracting unit in the irradiated area can be determined. 2) Method should be adaptable to the study of small areas. Depending upon the degree of preferred orientation in the specimens, it should be possible to obtain reliable data in a reasonable length of time on irradiated areas as small as 1.0 or even 0.1 mm in diam. 3) Method should permit direct correlation of crystallographic data with microscopic orientation data pertaining to crystallite axes, habit, morphology, and growth directions as determined by optical microscopy. 4) method should be such that selected areas of large specimens can be easily studied. Trepanning of a small specimen (such as an electron microscope specimen) from larger specimens was undesirable since it would greatly increase the problem of correlating the crystallographic and microscopic directional data. Requirements 3 and 4 dictated that an X-ray back-reflection pinhole technique should be used on large samples, such as metallographic specimens which had previously been examined and analyzed for their microscopic characteristics. Similarly, requirement 2 could be satisfied by choosing a collimator of appropriately small diameter. Exposure times would not be excessive provided the detector were close enough to the specimen. Because of space limitations film was chosen in preference to a Geiger counter. Requirement 1 was fulfilled by using monochromatic radiation and providing enough additional degrees of freedom in specimen rotation to compensate for Bragg law restrictions on diffracted beams. DESCRIPTION OF APPARATUS The apparatus shown in Fig. 1 consists of a pin-hole collimator, (a), projecting through a rotatable circular film in a holder, (b), which records X-ray reflections in the back-reflection region. The specimen, (c), is mounted on the end of a shaft, (d), which is provided with an adjustment, (e), so that the specimen surface can be placed accurately on

Jan 1, 1962

By Paul M. Tyler, Herbert R. Mosley

Strategically situated in almost the heart of the leading fertilizer-consuming area of the United States, Tennessee long has ranked second only to Florida as a phosphate-producing state. Since 1932 its share of the national output of phosphate rock has increased steadily, and in 1937 its production mounted to an all-time record. More significant even than the increase in tonnage are the forward strides in technology. The Tennessee Valley Authority's research program has led to quasicommer-cia1 operations using hydroelectric power to manufacture concentrated phosphatic fertilizer that is used to further the farmer education program designed to streamline the fertilizer business and halt the appalling waste of farm land by soil erosion. Even more stimulating to chemically minded imaginations is the production of elemental phosphorus by a private company that not only has succeeded in extracting it from the phosphate rock in electric furnaces but actually has contrived to capture it and to transport it safely in tank cars. New values have been created for low-grade phosphate deposits, and the economic life of reserves has been lengthened while the waste of former years goes back into the mills for recovery of its values by modernized methods. Tennessee's phosphate-mining industry dates from the discovery of blue rock in Lewis County in December 1893. Its known reserves are of the order of 101,500,000 tons, which compares with the production of 825,099 tons in 1937; that is, 21 per cent of the phosphate-rock output of the whole nation. The total output reported from 1894 until July 1. 1938, was approximately 19,000,000 tons. Offcial estimates of reserves are overly conservative and evidence submitted before a joint Congressional committee in November 1938 places "probable" reserves at more than 6,000,000,000 tons.

Jan 1, 1942

By Herbert R. Mosley, Paul M. Tyler

Strategically situated in almost the heart of the leading fertilizer-consuming area of the United States, Tennessee long has ranked second only to Florida as a phosphate-producing state. Since 1932 its share of the national output of phosphate rock has increased steadily, and in 1937 its production mounted to an all-time record. More significant even than the increase in tonnage are the forward strides in technology. The Tennessee Valley Authority's research program has led to quasicommer-cia1 operations using hydroelectric power to manufacture concentrated phosphatic fertilizer that is used to further the farmer education program designed to streamline the fertilizer business and halt the appalling waste of farm land by soil erosion. Even more stimulating to chemically minded imaginations is the production of elemental phosphorus by a private company that not only has succeeded in extracting it from the phosphate rock in electric furnaces but actually has contrived to capture it and to transport it safely in tank cars. New values have been created for low-grade phosphate deposits, and the economic life of reserves has been lengthened while the waste of former years goes back into the mills for recovery of its values by modernized methods. Tennessee's phosphate-mining industry dates from the discovery of blue rock in Lewis County in December 1893. Its known reserves are of the order of 101,500,000 tons, which compares with the production of 825,099 tons in 1937; that is, 21 per cent of the phosphate-rock output of the whole nation. The total output reported from 1894 until July 1. 1938, was approximately 19,000,000 tons. Offcial estimates of reserves are overly conservative and evidence submitted before a joint Congressional committee in November 1938 places "probable" reserves at more than 6,000,000,000 tons.

Jan 1, 1942

Jan 1, 1954

By Charles W. Goodale

The ores of the Butte district present a variety of combinations, and their treatment by concentration is an interesting study. They may be classified in general as follows: 1. Copper-silver ores, which are produced by the mines of the Anaconda group, and by the Mountain View, Colusa, Silver Bow and Parrot. The high-grade ores from these properties are roasted and then smelted; but a large proportion of the output is low-grade and siliceous, and hence requires concentration. The copper-bearing minerals are chalcocite, bornite, enargite and chalcopyrite, in varying proportions in the different mines, the gangue, which breaks readily into grains, being quartz and feldspar. 2. Silver-copper ores, of which the Gagnon vein is the largest producer. The grade of the ores from this mine is such that nine-tenths of the output requires concentration. The silver- and copper-bearing minerals of this vein are massive wurtzite, sphalerite, bornite, chalcopyrite, pyrite, tetrahedrite, enargite, tennantite and galenite, with a quartz gangue associated with feldspar and small quantities of barite and fluorite. The gangue is very hard and not at all granular. 3. Silver-ores containing a small amount of gold, embracing the product of the Alice, Magna Charta and Moulton claims, on what is known as the Rainbow lode, and that of the Lexington, Blue Bird, Nettie, Burlington and other mines. The gangue is quartz, carrying pyrite, sphalerite, galenite, tetrahedrite and argentite, with manganese in the form of rhodochrosite and rhodonite. Good results on ores of this class cannot be obtained by concentration, because large percentages of the silver-bearing minerals are disseminated through the gangue in such minute grains that even the finest practicable crushing

Jan 1, 1897

J. H. HEGINBOTHAM, a, metallurgist of the General Engineering Co., talked on "Current Milling Practice at Kirkland Lake," at the December meeting of the Utah Section. The ore is enough alike through the whole district so that some generalizations and comparisons may be made. The question as to whether or not the flotation process should be used in the flowsheet for extracting gold by cyanide solutions is still being vigorously debated, and it will seemingly need some years for a definite answer to be given. Most of the gold is either free, though much of it is finely dispersed in quartz, or occurs with pyrite. At times there may be 2 per cent of telluride compounds in the ore, but the amount of gold telluride present is small and has not been definitely established. It has been shown by Dr. Haultain and others that though gold tellurides may be so finely disseminated that it is necessary to grind the ore exceedingly fine, the compounds themselves are not difficultly soluble. (An increase in temperature helps to dissolve tellurides, and also to settle pulps.) It is likely that if the ore were ground through 400 mesh, practically all of the gold would be soluble. As it is, with 96 to 98 per cent of the ore ground to minus 200 mesh, and some 70 per cent minus 325, the cost of

Jan 1, 1934

By C. R. Kuzell

ALTHOUGH furnaces constructed of refractory brick have been oper-ated for many decades, there has always been an unfulfilled desire by the operators for a less arduous and more satisfactory method of patching weak spots and burned-out zones in order to postpone and to effectively extend the termination of a furnace campaign. Not only has this desire frequently arisen when small spots have approached incipient failure while the furnace structure as a whole was still in good condition, but also when larger areas showed signs of needing replacement. The availa-ble methods have been arduous, sometimes dangerous, inefficient with respect to the life of new refractory material used, and nearly always have necessitated interruption of the continuity of the furnace operations and therefore reduction in furnace production during the period of time required for the repair work. Most of these older methods have involved the replacement of masonry by refractory shapes in the weakened areas. Many attempts have been made to develop a method of patching the burned-out areas by spraying granular refractory material upon old surfaces. While some success has been attained in attempts to renew the grooved, corroded side walls and fettling, and the edges of hearths, there have been no known successful applications of the spraying method in patching the underside of arches of operating furnaces. The method developed recently at the Clarkdale smelter of the United Verde Branch of Phelps Dodge Corporation, at Clarkdale, Ariz., and described in this paper, has been found to be not only convenient and successful with respect to patching vertical or inclined surfaces, but has met with a marked degree of success in patching the parts of furnace arches that are exposed to flame, the successful result being obtained with-out interruption or interference with the continuity of furnace operations. ? It may be described as a method of renewing the interior refractory sur-faces of operating furnaces by pneumatic spraying of an aqueous suspen-sion of finely divided particles of refractory material. It has been used

Jan 1, 1939

Jan 1, 1918

By Albert Sauveur

(New York Meeting, February, 1913.) IT is delightful to read a technical paper like that of J. E. Johnson, The Effect of High Carbon on the Quality of Charcoal-Iron, presented in October, 1912, at the Cleveland meeting of the American Institute of Mining Engineers.1 The clear, simple, and straightforward manner in which he describes his experiments and results makes you feel as if you had been, so to speak, at his elbow during the course of his investigations, while his method of procedure is so rational that you can fairly anticipate each step in the logical sequence of the tests performed. The following notes suggested by Mr. Johnson's paper are presented here in the hope that they may help, if only a mite, towards the final solution of a problem of considerable scientific and industrial importance.

Jan 3, 1913

By Shosei Serata

Stress control methods of mining have been developed separately in at least four different parts of the world in entirely different types of mining -- coal, trona, salt and potash -- during the decade of the 1960s. They all utilized yield pillars as tools for ground control. Today, yield pillars are becoming widely used in under- ground mines in a variety of geological conditions. Stress control methods are effective in stabilizing openings in weak, complex grounds, especially at greater depths. Their advantage is that they utilize existing ground media to stabilize mine openings by altering the stress distribution patterns around the openings, by controlling design parameters such as room width, pillar geometry, and excavation sequence, rather than by using a conventional means of artificial ground support such as roof bolts, cribbing, or arches. Stress control methods, therefore, are suitable for both advance and retreat mining, including total extraction mining. Adaptation of these methods results in substantially greater safety, productivity, and ecnomy over conventional methods. These methods are based on scrutiny of the actual stress conditions in the ground, by both in-situ measurement and computer simulation. This paper provides a summary of stress control methods as developed over the last ten years. The field examples are limited largely to salt and potash mining applications, although the method has been used successfully in other mining applications. The examples illustrate that stress control methods actually address general ground weakness problems -- separation at discontinuity planes, swelling by shale expansion, deterioration by brittle fracture, and interference by ground water. That is, although the principle is developed mainly with reference to salt and potash applications, it is generally applicable to weak ground.

Jan 1, 1983

By Henning Nielsen

SIX weeks ahead of schedule, the International Nickel Co. of Canada Ltd. has brought a 30-mile rail line into the newly born town of Thompson, Manitoba. Its construction spurs the development of a rich new mining region slated to become the world's second largest nickel-producing area-exceeded only by Inco's Sudbury, Ont., workings. Two mines, the Thompson and the Moak Lake, will be opened to meet International Nickel's scheduled annual production goal of 385 million lb of refined nickel by 1961. Accomplishment of this aim will mean an additional 75 million lb of the metal available to consumers. In addition, stepped-up out- put of Inco's Sudbury holdings may increase this figure by another 25 million lb. (For an earlier report on these developments see MINING ENGINEERING News, January 1957).

Jan 12, 1957

By E. G. De Coriolis

THE development of huge production facilities and of new or improved processes for manufacturing magnesium from its raw sources has been an outstanding achievement of this war. Furthermore, at least one new method has reached a stage of pilot production that offers promise. Its potentialities seem to indicate that a reduction in cost and simplification or elimination of problems incident to the use of at least one of the present processes are quite within the realm of possibility. Although magnesium of very high purity (99.9 per cent and higher) is obtained, and the rate of recovery reasonable (60 to 70 per cent), the ferrosilicon reduction process is open to a serious objection, which at the time its use was proposed was thought to be sufficient to raise some doubts as to its success, at least on a high production basis. The temperature range at which the reaction is carried out-namely, 2100° to 2150°F.-is very close to the failure temperature of the material of which the retort is made. It is so close that for a time it was assumed it might make commercial use of the process an impossibility. However, at the time under discussion, the demand for magnesium was so great that it was felt by those who had to go ahead and produce this essential metal that the emergency warranted their taking a chance on this process. Subsequent developments have fully justified the soundness of their decision. Fortunately for the war effort, when the plants were put into operation it was discovered that although the retorts did collapse in rather short periods of time, as predicted, they could be blown back into operable shape by application of high-pressure air. This practical method of operation so relieved the situation that the problem disappeared. Nevertheless, if the process had not been successful, or the production of magnesium by the electrolytic process had not been able to keep pace with demands, our war program would have been seriously impaired. "FIRELESS COOKER" PROCESS For this reason a program was set up and assigned for the development of a new method that had been suggested to the War Production Board in 1941. It is believed justifiable in terming the method "new" for several reasons: (1) while utilizing the same (ferrosilicon) process as the Pidgeon, hence involving similar reactions, the type of retort or furnace is essentially different, (2) the method of operation, reaction temperatures, etc., differ materially, and, most important of all, (3) the problems to be overcome in making the process successful were not and could not have been anticipated by anything previously known about the Pidgeon process. As will be shown later, the briquetting process, the condenser, the furnace lining

Jan 1, 1945

By Edwards Wichers

The purpose of this paper is to set forth the matters of principal interest in connection with work done in the past few years on the purification of the metals of the platinum group, including the study and modification of methods already in the literature and the development of new procedures. For the most part, the results will be given in summary form, reserving the publication of detailed data and directions for a forthcorning paper to be issued by the Bureau of Standards. In recent years increasing interest has been shown in the preparation of the pure platinum metals, both by those concerned with the manufacture of the metals and their alloys for scientific and industrial purposes and those who are engaged in the study of the chemical or physical properties of the elements. The purification of the metals usually has been regarded as a matter so involved and difficult as to require the attention of specialists. It is hoped that this paper will show that any of the metals can be prepared in any desired degree of purity by relatively simple straightforward chemical methods. For the most part, it is thought that the methods given are suitable for small-scale refineries as well as for the laboratory; also, that they will bring the time required for the purification of any of the metals within reasonable limits. The new procedure suggested for purifying platinum should prove to be much shorter than any methods described in the literature. Treatment of Platinum Ore As is well known, the principal source of the platinum metals is a mixture of several native alloys of the metals, found chiefly in naturally concentrated deposits in stream beds or alluvial material. Without attempting to enumerate all of the minerals present, it may be said that the concentrated ore from such sources contains all of the six platinum

Jan 1, 1928

By H. Kazemi

An ideal theoretical model of a naturally fractured reservoir with a uniform fracture distribution, motivated by an earlier model by Warren and Root, has been developed. This model consists of a finite circular reservoir with a centrally located well and two distinct porous regions, referred to as matrix and fracture, respectively. The matrix has high storage, but low flow capacity; the fracture has low storage, but high flow capacity. The flow in the entire reservoir is unsteady state. The results of this study are compared with the results of the earlier models, and it has been concluded that major conclusions of Warren and Root are quite substantial. Furthermore, an attempt has been made to study critically other analytical methods reported in the literature. In general, it may be concluded that the analysis of a naturally fractured reservoir from pressure transient data relies considerably on the degree and the type of heterogeneity of the system; the testing procedure and test facilities are sometimes as important. Nevertheless, under favorable conditions, one should be able to calculate in-situ characteristics of the matrix-fracture system, such as pore-volume ratio, over-all capacity of the formation, total storage capacity of the porous matrix, and some measure of matrix permeability. INTRODUCTION The analysis of flow and buildup tests for obtaining in-situ characteristics of oil and gas reservoirs has received considerable attention in the past decade. Most of the available techniques result in reliable conclusions in macroscopically homogeneous reservoirs or in the homogeneous reservoirs with only certain types of induced and/or inherent heterogeneity (such as wellbore damage, etc.). In general, the greater the degree of heterogeneity, the less the reliability of the information deduced from the pressure transient data. A commonly encountered heterogeneous system is a naturally fractured reservoir where two types of distinct porosities occur in the same formation. The region containing finer pores may have high storage and low flow capacities. This is called the matrix. The remaining region may have high flow capacity with low storage. The latter region is generally the set of interconnecting fractures and fissures of the rock, and for this reason it is called the fracture. Ordinarily, we wish to obtain the permeability and porosity of each region and perhaps the frequency of the fracture distribution in a reservoir. Such information is necessary for reservoir engineering. Other information, such as wellbore damage, will be useful in evaluating possible remedial work for such fields. Few authors have suggested theories to aid in calculating the in-situ characteristics of a naturally fractured reservoir similar to what we have described above. Pollardl suggested that a naturally fractured reservoir contained three distinct regions: a damaged or an improved region surrounding the wellbore, and the two remaining regions the same as described earlier. He suggested that the flow was taking place from the tight matrix into the highly conductive fractures, then into the we wllbore region and finally into the well column. He concluded that the average pressure buildup in each of these distinct regions can be expressed approximately in terms of an exponential decay function of time. He also hypothesized that the decay coefficients for each of these functions were significantly different from each other; consequently, each of these functions became dominant in turn, in the process of pressure buildup. Thus, by a proper graphic plot of the logarithm of wellbore pressure differences vs buildup time, each of these functions could be determined (see Fig. 1). Pollard suggested methods of determining the wellbore damage and fracture volume. Later Pirson and Pirson2 extended

Jan 1, 1970

By Robert Sisselman

Dramatic changes have been effected since 1955 in the mode of iron ore shipments within the U.S. In 1955, less than one percent of ore consumed in domestic blast furnaces-approximately 125 million long tons-consisted of pellets. Five years later, in 1960, some 94.8 million tons of ore were consumed, 14% in the form of pellets. Projections for 1980 reinforce confidence in this most economic of blast furnace feeds, and set U.S. pellet consumption at 151.2 million tons. In the last decade, pellets caught fire in other countries. By 1969, world production reached 96 million tons. This compares strikingly with present world output of 154 million tons.

Jan 9, 1973

THE decades immediately before and after the end of the nineteenth century (1890-1910) were a period of increased activity in mineral industry education. One reason for this, undoubtedly, was the rapid increase in mineral production in the decade 1880-1890; pig iron and copper production tripled; coal, lead, and zinc output more than doubled. Most of the other mineral substances followed the same general trend. Aluminum production began in 1886; petroleum output, which in 1888 was less than it was in 1882, almost doubled in the next three years. Gold alone showed no appreciable change until its discovery at Cripple Creek in 1891, followed by the Klondike in 1896, brought to boiling a public interest in minerals that had been simmering for some years previously. The first cyanide plant in the United States was erected at Bodie in 1892, and the first chlorination plant at Cripple Creek* the next year. Silver- lead smelting had already greatly developed, and the metallurgy of copper was almost transformed. The hearth area and smelting capacity of copper reverberatory furnaces more than quadrupled between 1878 and 1894; matte converters were first erected at Butte in 1884. Copper production of the United States in 1899 was 20 times that of 1872. While it was the increased technology used in mineral production that really made the field attractive for educated young men, undoubtedly they did not realize that, and were impressed mainly by the quantitative increase in output. Another factor was the increased general interest in engineering education; three times as many men took engineering degrees in the United States in 1890 as in 1880; 1892 showed almost a 56 per cent increase over 1890. Industry had come to recognize that technical training was worth while. The mineral industry lagged somewhat at first; the total number of mining degrees

Jan 1, 1941

By T. A. Rickard

In a former paper* the writer has described the essential features of the general geology of the Cripple Creek region. In the present account it is intended to examine into the occurrence of the ores, the value of which has made this district the most important among existing American gold-fields. The production of Cripple Creek from its discovery, in 1891, to the close of 1901, has reached a valuation of fully $125,000,000. During the past year (1901) the output amounted to $17,285,470. In 1900 it was $18,174,681. The first discoveries, which led to the development of the district, were made in the spring of 1891, but it was not until 1893 that vigorous work was commenced. A great impetus was then given to the exploration for gold on account, of the sudden drop in the market-price of silver, caused by the closing of the Indian mints in the summer of that year. This induced an energetic population from the older silvermining camps of Colorado to go to the new gold-field, which was then beginning to attract attention. Prospecting, at first, was hindered by the comparative absence of outcrops, due to the fact that the surface of the hills is covered with a considerable thickness of shattered rock, resulting from the action of frost at a high altitude; but so much indiscriminate digging was done that a number of rich veins were uncovered, and this stimulated the search for others. The advanced condition of the mining industry of Colorado offered unusual facilities for exploration and reduction; progress was therefore rapid, with the result that the district soon achieved great prominence.

Jan 1, 1903

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Jan 1, 1938

By H. J. Morel-Seytoux

The influence of patten, geometry on assisted oil recovery for a particular dispIacement mechanism is the object of investigation in this paper. The displacement is assumed to be of unit mobility ratio and piston-like. Fluids are assumed incompressible and gravity and capillary effects are neglected. With these assumptions it is possible to calculate by analytical methods the quantities of interest to the reservoir engineer for a great variety of patterns. Specifically, this paper presents (1) very brieily, the methods and mathematical derivations required to obtain the results of engineering concern, and (2) typical results in the dorm of graphs or formulae that can be used readily without prior study of the methods. Results of this work provide checks for solutions obtained from programmed numerical techniques. They also reveal the effect of pattern geometry and, even though the assumptions of piston- like displacement and of unit mobility ratio are restrictive, they can nevertheless be used for rather crude but quick, cheap estimates. ,These estimates can be refined to account for non-unit mobility ratio and two-phase flow by correlating analytical results in the case M = 1 and the numerical results for non-piston, non-unit mobility ratio displacements. In an earlier paper1 it was also shown that from the knowledge of closed form solutions for unit mobility ratio, quantities called "scale factors" could be readily calculated, increasing considerably the flexibility of the numerical techniques. Many new closed farm solutions are given in this paper. INTRODUCTION BACKGROUND Pattern geometry is a major factor in making water-fIood recovery predictions. For this reason many numerical schemes have been devised to predict oil recovery in either regular patterns or arbitrary configurations. The numerical solutions, based on the method of finite difference approximation, are subject to errors often difficult to evaluate. An estimate of the error is possible by comparison with exact solutions. To provide a variety of checks on numerical solutions, a thorough study of the unit mobility ratio displacement process was undertaken. To calculate quantities of interest to the reservoir engineer (oil recovery, sweep efficiency, etc.), it is necessary to first know the pressure distribution in the pattern. Then analytical procedures are used to calculate, in order of increasing difficulty: injectivity, breakthrough areal sweep efficiency, normalized oil recovery and water-oil ratio as a function of normalized PV injected.

Jan 1, 1967