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By Richard T. Newcomb

This paper considers the many problems involved in estimating rates of technical change via productivity indexes. In mining, declining ore grades complicate the measurement of progress considerably. The estimates discussed in this article were made for the United States iron mining industry by means of two techniques: a simple model of production with two inputs, and multiple regression. The results can be used to explain the relation existing on U.S. iron ranges between rates of exhaustion, technical change, output per man and the increase in capital proportions observed since World War I. Similar ob-servations can be made on the mining sector trends in the United States, Canada, and Japan. Formidable problems confront the economist attempting to estimate the influence of technological changes on the progress of mineral industries. Peculiar to these industries is the problem of how to adjust any measure of technological progress for the offsetting influence of exhaustion. Exhaustion has long been recognized in the mining industry as a critical dimension. Empirically, it is usually treated as a problem of declining grades of ore either in production or in reserves. There are studies of the trends in mining industries attempting to relate changes in input requirements to changes in grade and technology over time. Most frequently, the measure used to indicate technological progress is average labor productivity, e.g., output per man-hour. However, although such an approach has the merit of being simple and direct, it ignores the influence of other important factors of production such as capital. Without defining both the nature of technological change and of production, it can be very misleading to identify increases in labor productivity with tech-

Jan 1, 1969

By B. W. Vallat

The Newport mine, located at Ironwood, gogebic county, Mich., on the Gogebic iron-range, is owned and operated by the Newport Mining Co., for the mining of iron-ore. I. GEOLOGY. The general geology of the gogebic range has been determined and recorded at different times by well-known geologists,' and their work will be referred to briefly in connection with the local conditions in the mine. The strike of the formation across this property is about 15" north of east. The general dip is 68" to the north. At the base of the formation on the aouth lies the granite. Looking north, at right angles to the strike of the formation, we have the foot-wall of quartz-slates and quartzite about 400 ft. wide; the iron-formation about 800 ft. wide, and the hanging-mall of black slates. The iron-formation is composed of banded jasper and quartzite together with iron oxide and concentrations of iron-ore. In character the ore iu a soft red hematite, with occasional masses of hard blue "steel ore." The formation is crossed in many places by diorite dikes, which cut through at various angles, the larger or main dikes dipping into the foot-wall in a SE. direction at angles varying from 15" to 30°, while numerous small dikes occur which strike through the formation in a vertical plane and at approximately right angles to the main dikes. There are various theories concerning these dikes, especially as to the time of their origin with relation to the ore-deposition. The commonly-accepted theory is that the dikes were there first, but there are some who contend that they were formed

Jan 1, 1912

By R. A. F. Penrose

I. INTRODUCTION. THE superficial alteration of ore-deposits is a recognized principle of geology, in the same way as is the superficial alteration of any of the common rocks. Its importance in some classes of ore-deposits is also well understood, as in many precious-metal deposits; while in other classes, its importance has been proved in individual cases, as in the Lake Superior iron-deposits. The causes and effects of superficial alteration in many classes of deposits, however, are not so generally understood; and it is the object of the present paper to show that such changes almost invariably give rise to exceedingly important chemical and physical phenomena, while in many deposits, the question as to whether they can or cannot be profitably worked depends largely on the extent and character of this alteration. The various treatises on ore-deposits published in the United States and Europe make frequent mention of superficial alteration, but have not treated the subject fully. As early as 1554, however, before which time but little accurate information was had on the geologic nature of ore-deposits, Prof. J. D. Whitney in his classic volume, The Metallic Wealth of the United States, describes the alteration-products, or gossans, in certain deposits and mentions others. On the more purely chemical side of the question, the work of Bischof, Daubrée, Roth, Rose, Hunt, Breithaupt, Blum, Julien, Deville, Debray, Volger, Moissan, Fremy, Lévy, Fouqué, and others has afforded much valuable information and many useful suggestions. The chemical principles brought out by these various authors have been applied, to a certain extent, to the solution of the phenomena of

Jan 1, 1913

By E. T. Turkdogan, M. L. Pearce

The rates of sulfurization and desulfurization of calcium aluminate, silicate, and ferrite melts by CO + CO2 + SO2 mixtures at 1550°C are reported. It is shown that for melts 10 to 15 mm deep transport of sulfide ions within the melt controls the rate of sulfur transfer. The rate data from shallow melts, i.e., 1 to 4 mm deep, have been analyzed on the basis of a diffusion or a reaction controlled process and indications are that the both processes may play a part in controlling the rate of sulfur reaction. The rates of desulfurization of silicate XVEACTION equilibria between metals, metal oxides, and gases have received considerable attention in recent years. However, the understanding of and aluminate melts increase with increasing PCO2/PCO ratio in the gas stream, the effect being most marked for aluminate melts. The sulfide equilibrium data obtained from the present work are shown to be in accord with the results of previous studies. It is shown that carbon dioxide has a measurable solubility in silicate, aluminate, and ferrite melts. Consideration is given to the partial equilibria which control the directions and the rates of reactions occurring simultaneously in complex heterogeneous systems. the kinetics of heterogeneous reactions, particularly those occurring at elevated temperatures has not been improved appreciably. Almost all the metallurgical reactions occur in heterogeneous systems involving two or more phases. Although in many authoritative text books and original Papers the basic principles concerning the kinetics of heterogeneous reactions are clearly underlined, they are seldom used to the best advantage in kinetic studies, particularly those involving the metallurgical reac-

Jan 1, 1963

By Walter A. English

CONTENTS PAGE Introduction. By WALTER A. ENGLISH 1 Theory of Seismic Reflection Prospecting. By WILLARD H. TRACY 2 Instruments for Reflection Seismograph Prospecting. By ARTHUR NOMANN 9 Seismograph Field Operations. By FRANK ITTNER 15 Determining Geologic Structure from Seismograph Records. By P. C. KELLY 22 INTRODUCTION BY WALTER A. ENGLISH,* MEMBER A.I.M.E. THE four papers making up this symposum have been prepared espe-cially for those who have no knowledge of seismograph prospecting. To many people mathematics is a formidable subject, and many are discouraged from studying seismograph prospecting under the mistaken assumption that the mathematical requirements are severe. In the papers presented here there is not a single mathematical equation. We believe that considerable competence in dealing with some of the most important problems of this work can be attained without any mathe-matical training whatever. At the present time, there is a real need for interpretation of results by persons thoroughly competent to bring geologic experience and imagination to bear on data that are subject to multiple interpretation from a strictly physical viewpoint. Likewise, those charged with the responsibility of planning seismo-graph exploration campaigns would do well to become familiar with as . much as possible of the technical aspects of the work. They would then be in better position to judge of its success in individual cases. It has often been said that the seismograph is a new structure-finding tool for the geologists to use. Using a tool and using its product are two different things. One does not use an automatic screw-threading machine when he buys a box of screws at the hardware store. Neither does the geologist

Jan 1, 1939

In response to Dr. Ledoux's paper, a large number of metallurgical establishments and individual assayers expressed their willingness to co-operate in the plan he proposed. The necessary samples were prepared as follows : Matte.—A car-load of matte was put through a Blake crusher, then automatically subdivided into tenths by a Taylor and Brunton sampler, and one-tenth passed through Cornish rolls and through a 12-mesh screen. This was again subdivided by an automatic sampler into tenths, and a final tenth, representing 1 per cent. of the original lot, was finished by hand-sampling on an iron floor until 100 pounds remained. This was pulverized to pass a 40-mesh screen and then thoroughly mixed and divided in the presence of my assistant for distribution to the parties co-operating. Copper Borings.—These were taken from a lot of anodes, the dip-samples from several batches having been united, remelted and cast into a plate, which was proved by assay to be of uniform quality in its different parts. Borings from this plate were intimately mixed and divided in the presence of my assistant. Samples were sent out November 1,1894, with the following letter: New York City, November 1, 1894. Samples of matte and copper (about I pound each) carefully prepared in the presence of my assistant and sealed with his seal as below, are sent you by express for assay and report according to the plan of Dr. Ledoux. These samples are constituted about as follows: Matte. Copper. From. To. From. To. Copper, per cent.,.....50 60 ..........., Gold, oz. per ton,.....2 3 0.20 0.50 Silver, oz. per ton,.....100 150 140 180

Jan 1, 1896

By Charles P. Berkey, John B. Hastings

The reconnaissance of the Goldfield mining-district, describecl in this paper, was made in May and June, 1905, and, though this time was too short for a complete report, the work accomplished may serve as a basis for more thorough future research. Dr. Berkey has examined the rocks collected by me, and I am using his classifications. As a result of further field-work, and Dr. Berkey's examination of the rocks, this paper is an elaboration and correction of my views expressed in the Gold-$elm Sun, May 12, 1905. The sketch-map, Fig. 1, illustrates the geology of the Goldfield mining-district. Goldfield is an eruptive complex, consisting of alaskite (hinary granite), hornblende-andesite, hornblende-dacite, rhyolite, pyroxene-andesite, pyroxene-dacite (sometimes containing a small quantity of olivine), quartz-felsite, olivine-pyroxene-ande-site, and basalt. Considering this list to be arranged in the order of eruption, the age-sequence of the rocks conforms to Richthofen's law, formulated in 1868. From his observations in Europe and America, propylite, andesite, trachyte, rhyolite and basalt, occurring together, succeed one another. In a general way, the medium and the more acidic rocks precede the most basic—a result supposed by some to hare arisen from their position beneath the. surface, and due to a rude stratification by gravity in the original cooling magma during the older history of the earth, or to the same differentiation occurring during a quiescent (molten ?) period preceding eruption, being aided by the ease with which acidic rocks, mixed with water vapors, become fusible. In effect, the more basic and less re-

Jan 1, 1907

By Thomas T. Read

The purpose of the following research, as originally planned, was to investigate the influence of temperature upon the plate-amalgamation process. In order to consider the amalgamation process intelligently, it was first necessary to learn the nature of an amalgam. In the performance of this task it was found necessary to consult a large volume of literature and to perform experimental investigations. The conceptions of the nature of amalgams thus obtained have so important a bearing on the amalgamation-process as a whole, as well as upon the possible influences of temperature, that it was advisable to include them in the treatment of the subject. The broader title is therefore used, even though some features of the amalgamation process have been treated very briefly and others entirely omitted, there being nothing new to present regarding them and their development not required for a clear presentation of the matter in hand. I. Historical Introduction. Gold was one of the earliest metals known to man. Occurring in the metallic state, it could be picked up in nuggets or mashed, as gold dust, from the sand and gravel of streams. Interestiag descriptions of the processes employed in early times for the recovery of gold may be found in Pliny's Natural History and in the treatise by Agricola on ores and minerals. But little progress in the treatment of the ores of gold mas possible until efficient crushing machines were devised. This want was supplied by the introduction, about the beginning of the sixteenth century, of the stamp-mill to treat the ores of Saxony. Blanket-strakes, or similar devices, were used to catch the

Jan 1, 1907

L. D. Ricketts, New York, N. Y.-In recent years the metallurgical field of the copper industry has expanded greatly, the copper ores have become lean and diverse in character, and we are obliged to treat such ores on a very large scale. On the commercial side, the operating and consulting staffs of ,the great mining companies have been enlarged and organized, and no great capital expenditure is decided upon until it has been investigated and recommended by a highly organized force of specialists as a committee. I believe that in the scientific field and in the most valuable proceedings of our various societies the old idea of one-man point of view and one-man treatment of principle and detail together has been. splendidly developed and should continue, but for the advancement of our art we should deliberately discuss subjects among ourselves in order to do away with the idiosyncrasies of the individual and to gain a composite view representing the best thought of many men. In the development of new ideas leading to the introduction of new methods, the societies could enlarge their present great field of usefulness if such discussion be had, and in my opinion further great good could be done if a number of men of different qualifications and experience would join in preparing a joint book, each dealing with his particular problem, but consulting the other men. In this way individualism would be preserved and various processes would be described, and if properly reviewed the paper would be palpably capable of analysis, and the student would have at his command the associated efforts of a group of qualified engineers.

Jan 4, 1915

By C. B. Dudley

In October, 1878, and again in February, 1881, I had the honor to make public, through the medium of the American Institute of Mining Engineers, the results of an extended study of steel rails which had been in service, and which mere taken for the purpose from the tracks of the Pennsylvania Railroad Company. These studies appeared in three papers. In the first of these papers the question. what kind of steel is least liable to fracture or disintegration in the track, was the principal one considered. In the second paper the question discussed was, does the power of steel to resist wear increase with the hardness ? In the third paper the relation between wear and the chemical and physical properties of the metal was the principal point considered. The general results arrived at, or the cooclusions reached, were, as follows: 1. That a mild steel is less liable to fracture, and if properly made, less liable to crushing or disintegration in the track than a harder steel. 2. That the wearing-power of steel in rails not only does not increase as hardness increases, but, on the contrary, diminishes; or, in other words, that a mild steel gives less loss of metal under the same service than a hard steel. These conclusions may be briefly stated in a single sentence—namely, in rails mild steel is not only less liable to fracture and disintegration in the track, but it also gives longer life, or wears more slowly under the same traffic; than harder steel. It is perhaps hardly necessary to add that by mild steel is meant steel

Jan 1, 1891

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By T. A. Rickard

INTRODUCTORY. THE presentation to the Institute, eight years ago, of the paper of Pošepny on " The Genesis of Ore-Deposits " has borne fruit in much fresh: investigation, as is evidenced, for example, by the group of very valuable papers, by distinguished members" of the United States Geological Survey, read at the Washington meeting-discussions of general principles particularly suggestive to those who are engaged in mining. Pošepny, in the discussion of his famous treatise, said that the present writer seemed to look at every new conception in ore-deposition" from the sole standpoint of its immediate usefulness in mining."* Protesting mildly against " sole " and "immediate," I accept the impeachment. It calls for no defence. THE DEVELOPMENT OF RECENT THEORIES. Given the idea of an underground water-circulation as the chief factor in the deposition of ore, the next step in the inquiry as to the genesis of such deposits is, the endeavor to determine which particular part of the general water-circulation is responsible for the results. Around this question have centered the controversies of a generation, and to these controversies we owe the gradual clarification of our ideas upon the processes of ore-formation. It is unnecessary to sketch here their progress from Werner to Le Conte, who combated in 1883 the extreme views of the lateral-seeretionists, and in 1893 opposed the narrow interpretation of the ascensionist-theory. The generally accepted opinions of to-day are a well-deserved tribute to his philosophic discrimination. Thanks to Prof. Van Hise and Mr. Slichter, whose work he utilizes, we have now arrived at a comprehensive conception

Jan 1, 1902

An educated man is distinguished neither by his clothes nor by his knowledge; he is remarkable not for the things he says, but for the way he says them. You cannot even stand with him under an archway in the rain without finding him out. He may talk only of the weather. His words and his phrases alike my be simple. What distinguishes him is the arrangement of his words; however desultory his talk, it will be methodical; he has habituated himself to foreseeing the part to be played by each word he uses and the place to be taken by each sentence he utters. On the other hand, the uneducated man, though shrewd and well-informed, will relate facts and events as they recur to him, generally in disorder; in his effort to recollect and in his attempt to rectify forgetfulness he will pause irregularly, filling the intervals with meaningless phrases, such as "and then", "and so", or "said he to me", "said I to him"; and even the continuous parts of his story will be told confusedly-because he has not learned the proper use of words.* My own experience as an editor of technical manuscripts has taught me that the misuse of 'that' and 'which' is a fruitful cause of obscurity and confusion. The relative pronouns have distinct functions, and no writer can express himself clearly until he has learned to discriminate between these functions. For example : The engineers who refused to submit were discharged. The engineers, who refused to submit, were discharged. The engineers that refused to submit were discharged.

Jan 1, 1931

By J. C. Williams, M. J. Blackburn

MANY aspects of the formation of the metastable w phase in titanium-transition metal alloys have been described in several recent papers.1-4 These papers have reviewed earlier work on the w phase and have further defined most of the important features related to the formation of this phase, e.g-., its crystal structure, composition, and morphology. There are, however, several important points regarding formation of the w phase in titanium alloys which have been described in less detail. Two of these are the relationship between lattice misfit and w phase morphology and the influence of lattice misfit on the mode of formation of the equilibrium a phase. In this communi- cation we will present transmission electron microscopy results relevant to these two points. The alloys used in this study were prepared by non-consumable electrode arc melting, each 30-g button being remelted a minimum of twelve times. The alloy compositions we have studied are listed in Table I. Thin foils were prepared using standard techniques described elsewhere. Two distinct c' phase morphologies have been reported in earlier papers. The phase is ellipsoidal in the Ti-Mo3 and Ti-Nbl system and cubical in the Ti-V3 system. Results of the present study show that the w phase is also cubical in Ti-Mn, Ti-Fe, and Ti-Cr alloys as illustrated in Fig. l(b) to (d). Fig. l(a) shows the ellipsoidal morphology in Ti-MO3 for comparison purposes. It was suggested in an earlier paper3 that the w phase morphology may be controlled by the lat-

Jan 1, 1970

R. V. Norris, Wilkes-Barre, Pa. (communication to the Secretary*):—Mr. Stow's paper presents a series of arguments, numbered from 1 to 18, concerning the relative merits of four systems of colliery-ventilation, designated by the author as " plain pressure-ventilation," " plain exhaust-ventilation," " obstructed pressure-ventilation," and " obstructed exhaust-ventilation." These arguments are subsequently compared by means of tables, in which an arbitrary numerical value is assigned to each, and which consequently serve no other purpose than that of showing his opinions and predilections, as indicated by his assignment of the said numerical values. In addition to this general summary, Mr. Stow intimates his preference for a fifth method of colliery-ventilation—namely, what he calls " alternating pressure-ventilation," which consists in the running of the fan at "pressure " during working-hours, and as an " exhaust" between shifts—a system which he proposes as, perhaps, new, yet which he thinks deserves recognition " as a standard form." This proposed " standard form " is not to be found in practice ; and I think it would be impracticable in gaseous mines of large extent, for the following reasons: 1. It takes considerable time to reverse the air-current in a large mine; and the reversal would involve a period of complete stoppage of ventilation, long enough to permit serious accumulations of gas. 2. In shaft- and slope-mines, at least, it is hardly practicable to have " every man out of the mine" during the night, and certainly impracticable to avoid keeping mules and horses inside. 3. The doors necessary to divide and direct the air-current are properly hung to open against the air-pressure; and, unless

Jan 1, 1910

By Walter Harvey Weed

In a previous paper upon the enrichment of mineral veins by later metallic sulphides,? the writer has shown that certain masses of rich ores, such as are found in many mines, either near the water-line or as bonanzas in depth, are of secondary origin, and are due to a leaching of lean ore and the concentration of the material by reaction between the solution and the unaltered ore below. The geological and mineralogical evidence is believed to form an adequate basis for a chemical and physical explanation of the phenomenon. In the present paper the writer will give a brief synopsis of this theory, and will apply it more particularly to deposits of the precious metals, laying special emphasis upon the dependence of such enrichments upon the presence of iron sulphide (as pyrite, etc.) in the primary ore, and upon structural features which control the circulation of the enriching solutions below the water-level. It is believed that many, though not all, of the bonanzas arid pay-shoots of rich sulphide ores, especially those carrying gold and silver, which are encountered in ore-deposits, are of such secondary origin. Apparently it is essential that the occurrence and structural relations of such ore-masses should be understood, as the success of the mine is often dependent upon the finding and extraction of these ores. A legitimate deduction, too, is that such ore-deposits decrease in value With depth. As my own studies have been mainly in Montana, my illustrations must be drawn from the ore-deposits of this and adjacent States, with such as I have noted in hurried visits else-

Jan 1, 1901

Jan 1, 1940

By J. J. Becker

BEAN1 has discussed the magnetic behavior of mixtures of small ferromagnetic particles on the order of 20 to l000A in diam. As he points out, there are three size categories with characteristic properties: 1) Particles large enough to contain many ferromagnetic domains magnetize initially by the motion of domain walls. The initial susceptibility of such particles, if domain-wall motion is assumed to be perfectly easy, depends only on their shape. It is equal to the reciprocal of the demagnetizing factor (and is thus 3/4 tt for a sphere) and is independent of temperature. 2) Smaller particles find it energetically undesirable to contain domain boundaries. They are always spontaneously saturated, and reverse their magnetization only by rotation of their entire magnetic moment. As assemblage of such particles has a remanence which is a large fraction of the saturation of the assemblage; its coercive force is on the order of 2K/1,, where K indicates magnetic aniso-tropy from any source, and I, is the saturation magnetization of the substance of which the particles are made. 3) Particles which are still smaller continue to be single-domain, but the direction of their magnetization fluctuates thermally, as first pointed out by Neel.' They have no remanence and no coercive force and possess the temperature-dependent magnetization curve of a paramagnetic substance with a very large moment. Bean calls this superpara-magnetism. All of these kinds of behavior are observable in alloys consisting of a precipitate of ferromagnetic phase in a nonferromagnetic matrix. Fig. 1 shows a typical aging curve for the room temperature coercive force of a sample of 98 pct Cu-2 pct Co alloy

Jan 1, 1958

By J. J. Jakosky

The fundamental hydrodynamic principles governing the production of oil from wells have been carefully studied and evaluated by many investigators. These prior studies are quite complete and cover virtually the entire field of oil production and recovery.' One of the most important measurements in production studies is that of the bottom-hole pressure at various rates of production.2 It is the purpose of this paper to outline the technique and economics of fluid-level measurements as applied to pumping wells and to review briefly other methods for obtaining bottom-hole data. The applications of bottom-hole pressure or fluid-level measurements are based on simple hydrodynamic principles. Under equilibrium conditions, pbh = hd + pg + pch [1] when pbk = bottom-hole pressure, Ib. per sq. in. absolute, h = height of fluid in well, ft., d = average fluid density, Ib. per sq. in. per foot, p, = weight of section of gas column 1 in, square from fluid level to casinghead, Pch = casinghead pressure, Ib. per sq. in. absolute. In words, equation 1 states that the bottom-hole pressure is equal to the weight hd of the column of fluid plus the weight of the column of gas between the fluid and the casinghead plus the casinghead pressure. At moderate rates of flow, the rate of production is approximatcly proportional to the difference between the reservoir, or static bottom-hole. pressure and the flowing or producing pressure; i.e.: Q = c(pr - pbh) [2] pr = the reservoir pressure, c = the constant of proportionality. However, at production rates approaching zero and also at high rates the proportionality may break down. By combining equations 1 and 2 the

Jan 1, 1939