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By James F. McDivitt

The mineral industry of today is faced with a number of dilemmas, not the least of which grows out of the series of related facts-world mineral consumption is growing, and is expected to continue to grow; maintaining adequate capacity to meet needs will require very great capital investment over the next decades, investment which must be measured in billions of dollars; much of the new production must come from remote and relatively underdeveloped countries; many of the areas in which such development must take place are not areas in which private capital enters without some trepidation. There are real problems in financing new mineral development-problems which have occupied the thoughts of many in the industry. One group which is currently providing part of the answer, and perhaps pointing the way to further progress in the future, is the World Bank. Loans from the World Bank are arranged usually for countries which are attempting to develop their economies through expanded industrial production. More often than not they are for the development of electric power projects or transportation facilities. Although we consider the mineral industries to be basic factors in industrial development and very important factors in the early stages of development of a country, few of these loans are for mineral development-no more than a half dozen out of a total of well over 300 loans which have been granted to date. Yet the World Bank has played a far more important part in world mineral development than these figures would indicate. The few loans for mineral development which it has made are important, but of considerably greater importance are the secondary effects of many of the non-mineral development loans and some of the special services which the Bank also offers.

Jan 5, 1963

By Jack Parker

The White Pine mine site lies five miles south of Lake Superior in Ontonagon County, Mich. Copper sulfide, mixed with some native copper, is mined by a room-and-pillar system from gently dipping Upper Kewee-nawan sediments. Depth of mining now varies from 700 to 1800 ft and the ore body continues to a depth of at least 3400 ft. An area roughly 21/2 miles square has already been mined. Mining height has varied from 61/2 to 22 ft. A rock mechanics program was set up in late 1963 to promote safety and mining efficiency. This note reports some of the findings. Rock Strength Compressive strength of small, dry specimens of sandstones, siltstones, and shales from the ore zone varies from 20,000 to 30,000 psi. This is intermediate between the softer coal mine sediments and the meta-morphic and igneous rocks of hard rock mines. Annual Cycle of Rock Failure Since 1963, every roof and pillar failure involving more than a few tons of rock has been examined and documented. Some 1500 stations have been installed for measuring convergence, -c1/1000 in., with Invar extensometers. At first it was thought that there was some kind of a cycle of roof failures; perhaps annual, perhaps even elated to the moon or to earth tides, but records (see

Jan 1, 1971

By E. E. Carpenter

Believing that the results accomplished in the mill of the Churchill Milling Co., Wonder, Nev., during the fiscal year ended Sept. 30, 1914, will be of interest, I am presenting the more prominent facts and figures showing the progress made in treating this ore with especial reference to tonnage, supplies, costs, and extractions. The mill is situated at Wonder, Nev., in the Wonder mining district, 55 miles east from Fallon, Nev., the nearest railroad point. All supplies are hauled this distance by freight teams, this method of transportation having been found more reliable for continuous service than truclis, the price paid for hauling being slightly under one cent per pound. In this mill are treated the ores of the Nevada Wonder Mining Co. Ore is Unusually Hard The company which tested this ore before the mill was built reported "This ore is an unusually hard, tough, oxidized quartz, carrying a small percentage of high-grade sulphides, containing good values in both gold and silver. None of the rebellious silver minerals appear to occur in appreciable quantities." ... "In regard to the mill tonnage this ore is unusually hard and tough, and a high stamp duty cannot be expected. Using a 20-mesh screen and 1,050-lb. stamps, our best work was three tons per stamp per 24 hours." It is very probable that the ore delivered to the testing plant was harder than the regular mill run has proved to be. However, at present the mine is developed to a depth of 1,000 ft., and still shows hard ore in places at this depth in about the same proportion as on the upper levels from which the test ore came; during this year's work, ore was treated from nearly all levels. Together with this hard ore in the mill feed a considerable proportion appears to be broken down and tending to crumble, thus making an ideal mixture for stamp milling. A small proportion of talc is also noticeable, which sometimes increases in amount to the point where it is very troublesome in the thickeners.

Jan 1, 1916

By C. K. Leith

At the outset I would like to make it clear that I do not enter this discussion in a controversial spirit, but in an attempt to contribute something helpful to an understanding of a difficult problem. I have too high regard for the- sterling quality of the work of the men who have studied this subject in detail to offer anything in the way of essential contradiction to their statements of fact. Difference of opinion arises from differing valuation of the possible alternative hypothesis which these facts suggest. Some degree of recrystallization in limestone contact zones has been recognized by many investigators. Earlier investigators, for the most part, assigned an important, if not the most important, ro1e to recrystallization in development of these zones. With the growing recognition of introduction of ores and gangue materials into the contact zone from igneous rocks through the medium of primary magmatic solutions, there has been a tendency to ascribe to this process most, if not all, of the chemical and mineralogical characteristics of the contact zonc. This has involved a correspondingly diminished emphasis on recrystallization of substances already there as a factor in the process, and in some cases even the complete elimination of this hypothesis. From detailed study of a few contacts, casual observation of others, and a general familiarity with the literature, some of us have been led in recent years to raisc the question whether the pendulum has not swung too far away from recrystallization toward direct introduction from igneous sources, and to argue for more recognition of the part played by recrysta11ization.l The inevitable sequence has been that those of us who have .taken this view have been charged, at least by inference, with emphasizing recrystallization to the total exclusion of the alternative process. Scientists, like other men, like to classify and pigeon-hole views under simple and definite designations, leaving out qualifications which would tend to make the classification more difficult to state. This has made the problem seem more definite and simple, but has tended to obscure the fact that the disagreement is primarily not one relating to essential facts, but one of

Jan 1, 1915

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.'-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.' Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By Reginald S. Dean

THE commercial availability of electrolytic manganese has greatly changed the position of manganese as a nonferrous alloying metal. Manganese metal commercially available up to about ten years ago was reduced with either silicon or aluminum and contained substantial amounts of the oxides of these metals and other impurities. Manganese was accordingly not available as an alloy base and its addition to copper-base and nickel-base alloys was generally limited to a manganese content of a few per cent. Several special alloys like manganin contained up to 12 pct of manganese. A method for the production of electrolytic manganese was developed by the Bureau of Mines in 1936 and commercial production was begun in 1938. At the present time (June 1951), production is about 12 tons per day but appears likely to be substantially increased. Electrolytic manganese is deposited from an aqueous electrolyte containing manganese and ammonium sulphates and is marketed as cathode fragments about 1/8 in. thick. The impurities in its composition are as follows: iron, 0.0015 pct; copper, 0.001; arsenic, 0.0005; cobalt, 0.0025; lead, 0.0025; molybdenum, 0.001; sulfide sulfur, 0.017; sulfate sulfur, 0.014; insoluble, 0.002; carbon, 0.002; hydrogen, 0.015. These figures are from Bulletin 463, U. S. Bureau of Mines. From an alloying standpoint, the most important impurity is hydrogen. This can be removed by heating; 95 pct of the hydrogen can be removed in this way without introducing significant amounts of oxygen or nitrogen. Much of the commercial electrolytic manganese used in alloys is dehydrogenited by the producer, since the amount

Jan 1, 1953

By William A. Vogely

Mining employment in the United States declined from 986,000 employees in 1948 to about 600,000 employees today. This has occurred even though the Index of Physical Volume of Mineral Production (1957-59=100) has increased from 88 to 111 and the value of mineral production measured in constant(1957-59) dollars has increased from $14.7 billion to approximately $19.3 billion. Average unit mine value has increased 24% as compared with a 34% increase in prices in general. Apparent consumption has increased more than domestic production, indicating an increased dependence on imports. The mineral economy presents a complex pattern of development factors in the post-war period. This article presents a technique by which the various forces that have been acting on the market for a mineral commodity may be sorted out and by which the extent of the impact of technological change in use as well as the technological change in production can be measured. If one is interested in delineating fully and completely the impact of technological change upon the mining industries, it is not sufficient to describe the increase in productivity reflected by the above employment and production figures. What is reflected there is only the effect of technological change in the production function of the commodities under concern. These effects are obviously very substantial and have major implications for labor, capital and supplying industries. However, they are not the only effects of technological change and, in fact, may be relatively minor when the impact which arises because of changing technology in the using or consuming industries is considered.

Jan 4, 1965

By Malcolm V. Lowry

At Balmat in northern New York State, the St. Joseph Lead Co.'s 2100-tpd zinc mining and milling operation is utilizing a unique thickener in conjunction with conventional crushing, grinding and flotation methods. From 1930 through 1962, zinc concentrates went directly from flotation to the filtering, drying and loading facilities, all of which had to operate 24 hr per day. Wide fluctuations in tonnage also had to be accommodated due to variations in the grade of ore. Many problems were thus encountered in filtering and drying, but the cost of installing a conventional, large diameter thickener could never be justified. In 1963, after thorough investigation, an unconventional thickener that is unusual in several respects was installed at Balmat. The tank depth is 16 ft instead of the normal 8 ft. The rakes are raised and lowered by having the main drive gear located on a movable platform. Automatic controls are programmed to raise the drive platform and rakes during one shift of storage. During the next two shifts of withdrawal, the controls are programmed to lower the drive platform and rakes.

Jan 5, 1966

The Empire IV expansion is on schedule for completion in January 1980; Hibbing Taconite's 2.7 million ltpy* expansion should be finished late in 1979; and Reserve Mining's tailing disposal project is on target for April 1980. Erie Mining Co., the first to bring 170-ton haulage trucks to the Mesabi Range, reports excellent operating results, and Inland Steel expects to produce 80% of its pellets in 1979 using coal rather than oil. One Michigan mine has so many inspectors that it has hired a school bus to transport them around the operation; and a contractor reports that mine construction projects of the future may require the training of 15,000 workers. All of this was covered at the 52nd Annual Minnesota Section AIME Meeting and the 40th University of Minnesota Mining Symposium, a joint event held each January in Duluth.

Jan 3, 1979

With only one certain exception coal was never used by the Indians, before white men came to America, for any purpose except as an ornament or for paint. Within the past few years it has been discovered that the Hopi Indians in Navajo County, Arizona, used lignite for burning pottery, about 1000 A. D., as dated by tree rings. They were able to obtain a clear color in their ware that could not be obtained with brushwood fires. The coal was mined by hammers from outcrop openings, some of which can still be seen, and the tools used have been found in them.1 (See also p. 376.) Small figurines made of splint or cannel coal have been found at various localities in western New York, in Ohio and possibly other places, evidently made for ornaments. There is no reason to think they are of any greater age, if as old, as that mentioned above. Some crushed coal was used by the Indians as a black pigment in painting themselves, but apparently the eastern Indians never used coal for any other purposes. Some think that several tribes of Indians in the Northwest, along the Missouri, used coal as fuel, the basis being a statement attributed to Radisson about 1660. In the Jesuit Relations of 1659-1660 it was stated that Radisson anti Groseilliers had just returned from a visit to Lake Superior and beyond. "In the country of the Poualak, which means 'warriors' they say `as wood is scanty in supply and small in size in their country, nature has taught them to make fire with coal from the earth (charbon de terre) and to cover their cabins with skins.'"2 This statement was only hearsay with the good fathers, and the reputation for veracity of the two explorers is not of the best, and it is extremely probable that instead of coal they used turf, dry grass or buffalo chips. In fact in Radisson's Voyages' he does not mention coal at all in his account of the third voyage, when he was supposed to have seen it used. His accounts of his travels are badly mixed, and he and his companions were much better travellers than narrators. None of the early travellers up the Missouri River saw any evidence even then that the Indians were familiar with the use of coal. In the writer's opinion it is unlikely that coal was used as stated by the Jesuits.

Jan 1, 1942

Ocean environmental factors are an intriguing new set of parameters to be dealt with in the prospecting and exploration phases of resource development for both the continental margins and the deep ocean. While information and data gathering programs for ocean minerals would parallel onshore procedures, their costs generally run higher. Commercial Prospecting-Identification of Mining Sites Two modes of prospecting can be identified-commercia1 prospecting (in which the ultimate objective is to define potential mining sites), and scientific prospecting, which is conducted with different objectives in mind. For ocean exploration, both types of prospecting are carried out prior to the obtaining of any exclusive rights to explore and exploit a specific deposit. Deepsea's John Flipse adds: "Any commercial prospecting program should by its very nature require the freedom to search wherever minerals might occur with maximum flexibility."

Jan 4, 1975

By Jim V. Rouse

In situ mining and dump leaching has been practiced for years. Recent environmental concern over conventional mining and milling techniques has rendered in situ mining more attractive. While there are many environmental advantages to in situ mining, there are disadvantages which, if ignored, can lead to environmental damages, followed by stringent control. The environmental advantages and disadvantages of the various types of in situ mining operations are discussed. Current legislation and regulations governing in situ mining are cited, together with a suggested program of environmental monitoring designed to protect the mining company as well as the environment. Suggestions are made for possible solution of existing pollution problems associated with previous mining activities by heap-leaching techniques. Present and indicated control of subsurface injection is traced, because of the many similarities in philosphy and monitoring requirements to in situ mining.

Jan 1, 1974

By W. A. Hoyer, G. A. Lock

Laboratory and field tests have shown that it is feasible to log for copper in a qualitative way using the techniques of neutron activation analysis. Laboratory tests showed that the 0.51 and 1.04 mev gamma rays of 62Cu and 66Cu, respectively, could be diagnostic. However, in the core holes, the detection of copper was limited to 0.3% concentration because of interferences from the 18Si and Al gamma rays. Both stationary and continuous logs were made, but only the stationary data yielded a recognizable copper response. This response consists of a combination of two effects-the direct response from copper at 0.51 mev and an increase in low energy gamma ray absorption due to mineralization. Both low energy chemical (PuBe) and high energy accelerator neutron sources were used for the laboratory and field tests, while the same 2 X 5 in. Nal scintillation detector served for all the tests. Potential improvements in copper detection might be possible with solid state gamma-ray detectors which have better gamma ray resolution but much less detection efficiency. This type of activation logging requires complex equipment and trained personnel to conduct field operations and may find application where coring is difficult or prohibitive.

Jan 1, 1973

By N. J. Olson, G. W. Toop

A regular solution is characterized by a finite molar heat of mixing and entropy due only to ideal or random mixing. The thermodynamic properties of binary regular solutions which exhibit constant atomic coordination number and constant atom-atom intefac-

Jan 1, 1967

By Herbert Clark Hoover, Lou Henry Hoover

GEORGIUS AGRICOLA was born at Glauchau, in Saxony, on March 24th, 1494, and therefore entered the world when it was still upon the threshold of the Renaissance ; Gutenberg's first book had been printed but forty years before ; the Humanists had but begun that stimulating criticism which awoke the Reformation; Erasmus, of Rotterdam, who was subsequently to become Agricola's friend and patron, was just completing his student days. The Reformation itself was yet to come, but it was not long delayed, for Luther was born the year before Agricola, and through him Agricola's homeland became the cradle of the great movement ; nor did Agricola escape being drawn into the conflict. Italy, already awake with the new classical revival, was still a . busy workshop of antiquarian research, translation, study, and publication, and through her the Greek and Latin Classics were only now available for wide distribution. Students from the rest of Europe, among them at a later, time Agricola himself, flocked to the Italian Universities, and on their return infected their native cities with the newly-awakened learning. At Agricola's birth Columbus had just returned from his great discovery, and it was only three years later that Vasco Da Gama rounded Cape Good. Hope. Thus these two foremost explorers had only initiated that greatest period of geographical expansion in the world's history. A' few dates will recall. how far this exploration extended; during Agricola's lifetime. Balboa first saw the Pacific in 1513 ; Cortes entered the City of Mexico in 1520; Magellan entered the Pacific in the same year ; Pizarro penetrated into Peru in 1528 ; De Soto landed in Florida in 1539, and Potosi was discovered in 1546. Omitting the sporadic settlement on the St. Lawrence by Cartier in 1541, the settlement of North America did not begin for a quarter of a century after Agricola's death. Thus the revival of learning, with its train of Humanism, the Reformation, its stimulation of exploration and the re-awakening of the arts and sciences, was still in its infancy with Agricola. We know practically nothing of Agricola's antecedents or his youth. His real name was Georg Bauer (" peasant "), and it was probably Latinized by his teachers, as was the custom of the time. His own brother, in receipts

Jan 1, 1950

By Dean Edwin Dallin

A computer system was developed by Texasgulf's Corporate Data Center (at Raleigh, North Carolina) to evaluate the economics of proposed new projects and to determine the incremental expansion effects of existing projects. The Corporate Treasurer, Controller, and Senior Staff Members of the corporate office guided the project with advice from the Chairman's office. After consideration of commercially available programs, the decision was made to develop an in-house investment system. The main specification was that the program must do the accounting calculations on the computer exactly as done by hand in the corporate office. No average "approximations" or values were allowed. Also, the capability to change the calculation procedures quickly was a must. The experience gained in developing a program to evaluate Gulf Coast off-shore oil lease-bids was used to develop an investment system. Several ideas were taken from A Programming Language (APL) concepts. An investment functional language was developed, and computer programs were written to process the functional language. One feature is a print-out of the model in English. The English print- out assists the debugging and documentation of a model. The major expansion at the Kidd Creek mine was the test case for the new system. After the results were approved and accepted for the base case, many sensitivity runs were made. Numerous additional models were developed to reflect the investment opportunities at other sites. An existing edit program was used to build the models and to systematically organize all the data for different projects. Remote input-output capabilities were added to the system, allowing data to be prepared and submitted at one Texasgulf site with the results printed at another location within minutes. The project has been well accepted by Texasgulf's senior management. Growth of the system is now in the areas of (1) merging individual projects into the corporate financial statements, (2) use of classical forecasting to project future costs, and (3) coupling the investment program to mine planning and general ledger systems. Also, the system is now being installed on an interactive computer system to provide faster turn-around time and more flexibility.

Jan 1, 1977

By P. H. Dudley

In giving a brief account of the experiments in progress to inquire into some of the facts in regard to "railway resistances," recently commenced upon the Lake Shore and Michigan Southern Railway, with the dynagraph (which is essentially an instrument recording upon paper the force required to draw a train, at all speeds, marking the time in short intervals, so that the force absorbed due to any

Still, the subject of iron ore is associated in peoples' minds mostly with the Lake Superior region and this is as it should be. The Minnesota Section meeting exposed the forces that over a period of two decades, 1950 to 1970, are revolutionizing the industry. The Lake Superior region has been at the center of these changes and has been deeply affected by them. The rise of foreign sources of iron ore that did not require beneficiation and taxation considerations were for a number of years a giant setback for the Lake Superior region and Minnesota in particular. However, the companies in this region have led the drive to improve the quality of ores which are culminating in the tailored pellet. This is a product in which iron content, silica, without significant impurities, is manufactured for optimum blast furnace performance. The oxide pellet does not seem to be the end as partially or prereduced pellets are closer at hand.

Jan 3, 1966

By E. H. Griswold

The many complexities arising from our present oil pool proration systems emphasize the need for a suitable standard of property rights. Attempts at conservation and unitization agreements have frequently failed because of the lack of such a standard. The necessity of reducing production to consumption has caused umpires, committees, commissions and other governing bodies to allocate the production of flush fields among the respective owners. The methods of allocation vary widely and conservation of underground reserves is frequently neglected or misused. Critical economic conditions increase, rather than modify, competitive methods. In some fields we have irregular and uneconomically close well spacing. Many operators drill unreasonably large holes, take excessive sand penetrations or leave their wells untubed in order to secure higher potential open-flow tests than their offsets. All of these practices result in economic waste and frequently damage to the pool. Regardless of our agreement with the fundamental principles of proration or unitization, both are actual necessities in many of our present economic situations, and we are in urgent need of a suitable standard of rights to facilitate and simplify their operation. The problems pertinent to unit management are simple and of daily use in many partnership enterprises, but the problems of fair and proper division of production under either proration or unitization are, as yet, subject to controversy. The rights of respective owners must be ascertained and standardized before we can eliminate wasteful practices and still preserve constructive competition in our industry. Valuation of Tracts In a recent unitization conference it was found that each participant had a different basis for calculating the relative values of tracts. Some of these assumptions were as follows: 1. Unrestricted open-flow operation to abandonment. 2. Current proration system to abandonment.

Jan 1, 1933

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957