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By Reno H. Sales

Jan 1, 1914

Jan 1, 1907

IT will be recalled that when educational instruction for the mineral industry began at Freiberg, at the beginning of the eighteenth century, the original aim was to organize and systematize the procedures previously followed by young men in gaining familiarity with the technology then in use. There must have been many other ideas current, even then, as to just what a young man needed to learn in order to become capable of assuming responsibility for the supervision and direction of such technical work. The problem in Europe was decidedly different from that in nineteenth-century America, because some of the European mines were actually owned and operated by the governing authority and the others were supervised, regulated, and taxed by it. The American problem was the efficient performance of technical operations; the European one was regulatory supervision. It was natural, therefore, that in the development of educational processes in Europe stress was laid on those factors which conserved and protected the interests of the state. The study of mineralogy and geology, leading to correct judgments as to the workability and value of mineral deposits; assaying, which gave the means of quantitative measurements, as did surveying; chemistry, which furnished a better basis of understanding for assaying, mineralogy, and geology; and physics and mathematics, which are the bases for the understanding and efficient use of mechanical appliances, became the core of systematic instruction for the mineral industry. It was early recognized that men could learn more than was already known about all of these subjects and education took on that dichotomy which still characterizes it; the teaching of established knowledge to the unlearned, and that of extending of the bounds of knowledge, now loosely termed research, which after two and a half centuries of work still shows

Jan 1, 1941

By Arthur Taggart

THIS paper describes the result of a series of experiments run in the laboratory of the School of Mines, Columbia University, during the winter of 1927-28. It shows that the several operating adjustments of a pneumatic table produce effects in the action of a, given coal that may be grouped into two classes, viz.: stroke length, speed and rocker-arm angle, which affect longitudinal travel; air supply and table slope (transverse and longitudinal), which determine transverse travel. The magnitude of the effect of the different adjustments varies. Some of the adjustments affect stratification of the bed, both as respects size and specific gravity of the bed components, as well as direction of travel. Operation of a pneumatic table is fundamentally different from that of a wet table in that the former exerts, through the air supplied, a force on the particles upward away from the deck which is lacking on the wet table while, on the other hand, it lacks the positive control over cross travel that is supplied by the wash and feed water.

Jan 1, 1929

The ten-year "supply-demand relationship" tables in this chapter for various mineral and metal commodities have been adapted from Minerals in the U.S. Economy, compiled by the Bureau of Mines, U.S. Department of the Interior, published in 1975. Acknowledgment is made to the Bureau of Mines for compilation of the tables. [ ]

Jan 1, 1976

By R. S. Silo

A new process for leaching oxidized copper ore (CuO) is presented. Its principle advantage is that it requires low cost raw materials. For large operations the only materials used are sodium chloride (NaCl) and calcium carbonate (CaCO3). In those operations of medium size, sulfur, which is abundant in the North of Chile, is used. However the process may also be applied to small copper plants provided low cost sulfuric acid is available as a substitute for sulfur. That is, it may be applied to those small capacity plants where large additional installations for the regeneration of the leaching solution are not needed. The method is comprised of six stages, namely: Crushing, Leaching, Washing of the Solution, Precipitation, Regeneration of the Leaching Solution, and Fusion. A flow diagram for this process in a large or medium-sized plant is given. LEACHING This process requires hydrochloric acid as the leaching solution for treating copper ores. This is easily produced from sulfuric acid and sodium chloride as follows: A small excess of NaCl is advisable to avoid the presence of free sulfuric acid. The experiments reported here were performed with 36 grams of HC1 per liter of solution to obtain a free acidity equivalent to 50 gpl of H2SO4 (the usual leaching solution concentration). Hydrochloric acid leaching may be done by either of the usual methods; i.e. percolation or agitation. The method selected depends on the characteristics of the ore. No matter which method is chosen, low pressure air can be used either as an air lift for circulation of the solution, or for agitation of the pulp with "Pachuca" tanks. In either case, there are no problems with respect to oxidation. Leaching by agitation produces good recovery; but at times, the problem of high consumption of leaching solution or the overproduction of grinding slimes which interfere with contact between phases negates this advantage. The percolation method was used in this study. Percolation took place in four 15-liter containers, 11 1/2 in. diam. by 12 in. height, having hemispheric bottoms. Each container was fitted with a wooden bottom having 1/4 in- holes. The air lift was a 3/4 in. plastic tube 10 in. high. Air at 6 psi was supplied from a rotating laboratory compressor. 10 kg of ore were charged to the container and counter-current leaching was used. The leaching solutions were fed through the center pipe in order to use the ascending solutions to reject the air in the charge. The solution circulated through the air lift in order to facilitate the movement according to the increase in density produced by the reaction between the phases present. Specific observations made in this report cannot be generalized because the leaching characteristics are dependent on the nature of the ore used, the method of leaching, and the production of primary or secondary slimes while crushing or leaching.

Jan 1, 1967

By W. R. Crane

The support of roof in mines is dependent largely on the character of the top rock and its occurrence. The formations overlying the orebed in the Birmingham district are sandstone and slate. The sandstone occurs in beds of sufficient thickness to constitute important elements in the system of support; the slate is relatively strong but is thinly stratified. The alternating beds of sandstone and slate furnish an excellent combination in that the former are strong and the latter are impervious; however, their continuity is broken by jointing or slip planes. The thickness, and consequent weight of the overlying formations, is important in so far as the size and arrangement of pillars are concerned but may be relatively unimportant, temporarily at least, as a factor in the support of the roof. The position of the respective beds of sandstone and slate, their relative thickness, and their inherent weakness because of the occurrence of faults and folds, may exert a predominating influence on their support in place, which is affected only in part by the weight of the cover. The only mine in this district that operates under a cover of approximately 2000 ft. (1900 ft.) is the Shannon so-called "twin slope," situated 14,000 ft. southeast of the portal of the No. 7 mine of the Tennessee Coal, Iron, & Railroad Co. The conditions in this mine indicate what may be expected in other mines when the same depth is attained; in fact, the effect of pressure is shown in several mines that have not reached two-thirds of that depth. It is evident, then, that conditions affecting the support of roof will not improve but rather will become more difficult with the extension of the mines into the valley under a constantly increasing weight of cover. Further, the difficulties will probably be augmented by the occurrence of faults and other disturbed ground, the presence and position of which at present are largely unknown.

Jan 1, 1925

By J. E. Spurr

CONTENTS. [ ] I. INTRODUCTION. The region here discussed is that part of western Nevada in which, during the last few years, discoveries of rich gold- and

Jan 1, 1913

By J. T. Crawford

ALTHOUGH nearly 10 pct of the total tonnage of coal produced annually within the United States is handled by bulk freighters on the Great Lakes, very little of the detail connected with it has been published other than occasional newspaper stories and publication of tonnage statistics. Of the total tonnage floated on the Lakes each year some 10,000,000 is stored and distributed from the port of Duluth Superior, at the western end of Lake Superior commonly known as the Head of the Lakes. This port has the largest single area concentration of coal docks in the world. Since this area contains the largest ore docks, the largest movable material handling bridge, the largest and highest grain elevator and the largest coal briquetting plant in the world, it is entirely fitting and proper that here also should be located the largest coal dock and what we believe to be the worlds largest clam shell. Of the sixteen coal docks operated by ten companies, five are owned and operated by the North Western-Hanna Fuel Co. which has two docks on the Superior, Wis. water-front and three docks in Duluth, Minn. It is with these five docks that we are primarily concerned. GENERAL HISTORY In the summer of 1871 a small sailing vessel entered the harbor of Duluth Superior with the first commercial coal cargo. All the coal brought up that first year did not amount to more than 3000 tons. During the year 1877 the first dock equipped for handling coal was built in Duluth. Coal receipts increased to 52,785 tons in 1879 the first year for which an official record was kept. Since then the volume of water-borne coal to the Head of the Lakes steadily increased to a maximum of 12,688,321 tons in the year 1923. This tonnage was nearly equalled in the year 1927 and the next highest tonnage recent year was in 1946 when 10,105,703 tons were unloaded. The average annual bring-up over a ten year period 1938 to 1947 was 8,605,231 tons. Approximately 30 pct of the coal unloaded at the Head of the Lakes is handled over the docks of the North Western-Hanna Fuel Co. Competition of other fuels coupled with expansion of coal fields in the mid-west have held coal receipts for Duluth-Superior at a relatively constant figure during the last eight years although the total tonnage of coal floated on the Great Lakes has more than doubled in the past 25 years. From the shovel and wheelbarrow method of unloading early cargoes to the horsepowered windlass derrick with a wooden tub was but a short step. The first movable coal handling, steam operated,

Jan 1, 1948

By Glenn C. Waterman, Scott Hazen

3.1-1. Purpose. Development drilling is directed towards determining the grade, volume, and three-dimensional outline of a mineralized zone previously located by exploration. It is distinguished from exploration or reconnaissance drilling, which has as an objective the discovery of new mineralized areas. A development drilling and bulk sampling program should furnish the following information: 1. Geology of the mineralized zone. 2. Quantitative data on grade and tons of material within pertinent cutoff limits. 3. Physical size and shape of the deposit. Areas underlain by waste as well as ore. 4. Mineralogica1 and metallurgical characteristics of the ore. 5. I1hysical characteristics of the ore. 6. Hulk samples for metallurgical testing and grade check. 7. Data on other factors that could affect mining operations, such as ground water, ground conditions, etc. 3.1-2. Procedures. There are numerous methods and techniques that are used to acquire pertinent data on a potential ore deposit. The total cost and accuracy of a development program depends on significant evaluation of the geology, proper selection of a drilling method, thorough analysis of sample data, and accurate evaluation of all the information. Knowledge of the geology of the mineral deposit is important in planning the development testing program and in evaluating the data obtained from such a program. Exploration work usually provides some significant information on the general size, shape, thickness, grade, and geology of the deposit. In some cases no further data are needed; in many cases geological complexities suggested by the preliminary work require further geological study. Of considerable importance may be the following:

Jan 1, 1968

By W. A. Ver Wiebe

It is becoming increasingly apparent that the State of Kansas contains one of the largest reserve areas for oil exploration in the United States. During the year 1936 no less than 54 new oil pools were discovered by drilling. In addition, seven gas pools were found, which may develop into oil pools when deeper horizons are tested. Several old pools increased their reserves when production was found in lower strata. The data presented in Table 2 indicate that nearly 2000 wells were drilled in the state during 1936. Of these more than 1214 found commercial quantities of oil and at least 61 found marketable quantities of gas. The data are conservative because complete results on drilling are not available for the eastern part of the state. Ellis, Rice and Russell Counties share honors with a total of 10 new pools in each. Barton County is prominent with six pools; while those counties claiming fewer new pools are Clark, Ellsworth, Harvey, McPherson, Ness, Pawnee, Rooks, Stafford and Trego. Important additions to our gas reserves were found in Finney and Haskell Counties, which are north of the extensive Hugoton gas area and may some day be part of it. At the close of the year there were 17,317 wells in the state rating as producers. By far the larger share (14,000) were classed as strippers and allowed to flow 100 per cent of their potential capacity, thus accounting for 33,500 bbl. a day. The remaining wells, capable of producing from 15 up to over 6000 bbl. per day, were limited in output according to these amounts. The largest wells having a potential of from 3000 to 7000 were allowed to flow from 2 to 3½ per cent of their official potential capacity. The percentage rises until wells of 15 to 20-bbl. capacity have a rating of slightly over 83. On the basis of these calculations the total potential capacity of all wells was 1,667,814 bbl., and the daily amount allowed was 175,851. Nine of the pools most recently opened were still unable to market their oil and were classified as "shut-in" pools. Total production for the state for 1936 was somewhat over 58 million barrels. Striking Geological Data Some interesting geological data were uncovered by deep drilling during the year. The most remarkable bit of information is the discovery

Jan 1, 1937

By Dorsey A. Lyon, Robert M. Keeney

Page I. Introduction..........234 I1. Chemistry oF Copper Smelting...235 1. Native Copper Ores.......235 2. Oxide and Carbonate Ores....235 3. Sulphide Ores.......236 (a) Elimination of sulphur ...236 III. Reverberatory Copper Smelting...237 IV. Substitution of the Electric Furnace for the Reverberatory Furnace..................... 238 V. Smelting of Fine Michigan Native-copper Concentrates in the Electric Furnace.................. 239 1. Conclusions.................240 VI. Proposed Process for Electric melting of Fine Native-copper Concentrates.................. 241 VII. OrdINary Copper Blast Furnace 'Smelting......... 245 1. Prerequisites.................. 245 2. Losses .................... 247 VIII. Experimental Data on the Electric Smelting of Raw Sulphide. Oxidized and Carbonate Ores............. 248 1. Vattier's experiment................ 248 2. Wolkoff's experiments................ 249 3. Experiments of Stephan.............. 250 (a) Conclusions of Stephan ............ 251 IX. Smelting of Sulphide Ores in the Electric Furnace...... 251 1. Ores Treated.................. 252 2. Conclusions................... 253 X. ELectric Furnace vs. the Reverberatory Furnace and Blast Furnace as a Melting Agent.............. 253 XI. Smelting of Sulphide Ores without Roasting or Partial Pyritic Smelting............254 XII. The Electric Blast Furnace vs. the Copper Blast Furnace for Partial Pyritic Smelting.......259 1. Metallurgical conditions......259 2. Mechanical considerations......259 3. Comparison of costs.......260 (a) General considerations .....260 (b) Cost of plant........260 (c) Amount of electrical energy...260 (d) Cost of smelting.......261 (e) Cost of electrodes........262 XIII. The Use of the Electric Furnace in the Smelting of PyRITIc ORES : 262 XIV. Summary...................... 264

Jan 1, 1914

By Thomas MacFarlane

I. INTRODUCTION. AMONG the industrial enterprises which have, from time to time, been undertaken in our Dominion, few have been more uniformly unsuccessful than those which have had for their object the development of our mineral resources. These resources have not been regarded as insignificant. On the contrary, it is supposed that we possess in our ore deposits something more than mere points of mineralogical interest. Some people are enthusiastic enough to believe that our mineral wealth will yet occasion the establishment in our backwoods of happy and industrious communities, causing, in fact, our wilderness to blossom as the rose. These enthusiasts do not shut their eyes to the serious obstacles which at every stage interfere with the carrying out of mining enterprises in this country, and which tempt one to believe that no such enterprise can ever be conducted to a desirable end, but they entertain the conviction that as our capitalists, miners, and technologists reach the years of discretion, and handle our mines in an economical, vigorous, and judicious manner, and as our statesmen become alive to the necessity of fostering, without extremely protecting, our metallurgical industries, mines and furnaces will gradually prosper, and so develop as to become a tower of strength to our agricultural, manufacturing, and mercantile interests. The fact that our past experience does not generally justify such glowing anticipations makes one all the more anxious to put on record the history of a successful mine, such as the Silver Islet has, on the whole, been. My connection with its discovery and early development was a very intimate one, and I propose in this paper to sketch its history and character, and sum up the amount of silver it has so far yielded. An additional reason for the appearance of this paper is that the Transactions of the Institute contain only a few references to the Silver Islet Mine. Although this mine is reported successful, we have, of course, no guarantee that it will not fall a victim to the same influences which have

Jan 1, 1880

By C. Kolm, E. P. Warekois, S. A. Kulin

MUCH insight has been gained into the nature of the cold-worked state of metals in recent years through the use of modern X-ray techniques. These methods have revealed the existence of stacking faults together with regions of high internal strain and have provided means of measuring the atomic perturbations in plastically deformed metals. In view of the recent increased interest in the solid state, it is desirable to extend these techniques to the study of lattice imperfections introduced into semiconductors during plastic deformation. It is of particular interest to compare the state of imperfection sustained by metallic bonding with that sustained by the covalent bonding found in semiconductors. A knowledge of the imperfections which can exist in semiconductors is important from both a theoretical and a practical point of view since they can greatly influence many of the physical properties. In order to determine the possible existence of stacking faults in covalently bonded structures, precise measurements were made of the diffracted peak positions of plastically deformed germanium, gallium antimonide, and indium antimonide. These measurements were based on the theoretical treatment of Paterson1 and are similar to those employed by Warren and warekois2 in their studies of deformed a brass. In addition, diffraction peak profiles were measured on the annealed and plastically deformed materials in order to obtain information concerning the distribution of internal strains through the use of the Fourier methods developed by Warren and Averbach.3 EXPERIMENTAL PROCEDURES AND TECHNIQUES Because of the room-temperature brittleness of the semiconductors studied, it was necessary to plastically deform the materials at elevated temperatures. The brittle-ductile transition temperature ranges of GaSb and InSb are sufficiently low to permit hot-filing operations. Therefore, high-purity, polycrystalline GaSb and InSb were filed in an argon atmosphere at 400' and 300°C, respec-

Jan 1, 1959

By Frederick O?Neil

SCOPE OF THIS REPORT THE object of this paper is to describe the present status and possibilities of liquid oxygen as an explosive based upon the investigations, research and practical work of the Ingersoll-Rand Co., and of the Air Reduction Co., from early in 1922 to date. The following work was done. 1. A study of the history and physical theory of L. 0. X. as an explosive. (No attempt will be made in this paper to give the history or theory, as this has already been covered by the literature on the subject.) 2. An investigation of the use and the practice with L. 0. X. in the iron mines of Lorraine where L. 0. X. has its largest application in Europe. Although L. 0. X. is extensively employed in the; iron mines of Lorraine, many of the mines using it exclusively, and blasting with it a total of approximately three million tons of iron ore per year, the fact that the mining practice in Lorraine1 is to drill comparatively shallow holes and blast only a few holes at a time, renders the data obtained there of very little value in estimating the possibility of replacing dynamite with L. 0. X. in American mining methods. In fact, in the iron mines in Lorraine, L. 0. X. replaced black powder, or its equivalent. 3. Laboratory research work on properties of absorbent materials. 4. Work in the Bureau of Mines explosive laboratory at Pittsburgh, Pa., on the properties of L. 0. X. cartridges. 5. Practical work underground with L. 0. X. cartridges in the Witherbee-Sherman iron mines at Mineville, N. Y. 6. Practical work in the quarries of the Calcite Quarry Co., Myers-town, Pa. 7. Practical blasting in several quarries and open-pit mines.

Jan 2, 1926

By R. J. Pfister

The development of a water-input profile instrument based on the introduction of brine and fresh water into an input well with the electrical location of, the boundary developed between them is reported. Two methods are available in the use of this instrument to measure the foot by foot water-intake rates of the various sand strata: the moving boundary method in which variable well bore diameters can be determined and/or cancelled out and the constant boundary method. The type of results obtained and the relative advantages of each of these methods are described in detail. Representative data are included covering the use of this instrument in experiments involving selective acidizing, selective plugging, and selective shooting. In such experiments, this instrument has been used to diagnose the unfavorable distribution of water intake in input wells and also to determine the effectiveness of the resultant treatments. The data included also serve to illustrate the type of problems which can be studied with this technique. Introduction For ten years or perhaps longer a number of progressive water-flood operators have felt the need for some to to measure the foot by foot water-intake rates of various strata in water-injection wells. The primary need is to diagnose unfavorable water distribution in various strata and to evaluate the effectiveness of the corrective measures such as selective acidizing, selective plugging, and selective shooting. Previously described methods for obtaining this type of data were not considered entirely adequate.l,2 The profile equipment described in this paper embodies the separate introduction of brine and fresh water into the well at carefully measured and controlled rates and the electrical location of a sharp boundary developed between these fluids. At present this instrument is a research tool of value in determining the effect of various well treatments on an individual sand strata. lts primary use has been on wells in which different sections require different treatments (e.g., wells with an open sand to be plugged and a tight sand to be acidized)- It has, thus, made possible the determination of a rearrangement of the water intake of a well. The instrument can also be used to direct the treating material into a given zone. In completing a well the less permeable sands are shot more heavily with nitroglycerine in order to equalize the water intake between the permeable and less permeable sands. The extent to which such corrective shooting has been successful Can be determined by a water-input profile. The combined profile and well-bore diameters should also provide a method for determining the direction and effect of various selective shooting techniques. Equipment The essentials of the water-input profile technique for measuring the intake per foot of individual sand strata are the injection of a nonconducting fluid, water, at the top of the well and a conducting fluid, brine, through a separate string of

Jan 1, 1948

By R. J. Pfister

The development of a water-input profile instrument based on the introduction of brine and fresh water into an input well with the electrical location of, the boundary developed between them is reported. Two methods are available in the use of this instrument to measure the foot by foot water-intake rates of the various sand strata: the moving boundary method in which variable well bore diameters can be determined and/or cancelled out and the constant boundary method. The type of results obtained and the relative advantages of each of these methods are described in detail. Representative data are included covering the use of this instrument in experiments involving selective acidizing, selective plugging, and selective shooting. In such experiments, this instrument has been used to diagnose the unfavorable distribution of water intake in input wells and also to determine the effectiveness of the resultant treatments. The data included also serve to illustrate the type of problems which can be studied with this technique. Introduction For ten years or perhaps longer a number of progressive water-flood operators have felt the need for some to to measure the foot by foot water-intake rates of various strata in water-injection wells. The primary need is to diagnose unfavorable water distribution in various strata and to evaluate the effectiveness of the corrective measures such as selective acidizing, selective plugging, and selective shooting. Previously described methods for obtaining this type of data were not considered entirely adequate.l,2 The profile equipment described in this paper embodies the separate introduction of brine and fresh water into the well at carefully measured and controlled rates and the electrical location of a sharp boundary developed between these fluids. At present this instrument is a research tool of value in determining the effect of various well treatments on an individual sand strata. lts primary use has been on wells in which different sections require different treatments (e.g., wells with an open sand to be plugged and a tight sand to be acidized)- It has, thus, made possible the determination of a rearrangement of the water intake of a well. The instrument can also be used to direct the treating material into a given zone. In completing a well the less permeable sands are shot more heavily with nitroglycerine in order to equalize the water intake between the permeable and less permeable sands. The extent to which such corrective shooting has been successful Can be determined by a water-input profile. The combined profile and well-bore diameters should also provide a method for determining the direction and effect of various selective shooting techniques. Equipment The essentials of the water-input profile technique for measuring the intake per foot of individual sand strata are the injection of a nonconducting fluid, water, at the top of the well and a conducting fluid, brine, through a separate string of

Jan 1, 1948

By E. Hoek

INTRODUCTION Rock slope stability research has been in progress for the past four years at the Royal School of Mines in London under the sponsorship of a consortium of 23 companies* with interests in open pit mining. This paper reviews the principal aims and achievements of this research project. In order to assist the reader in following these details, the basic philosophy underlying the formulation and direction of this research project is discussed. DISTRIBUTION OF RESPONSIBILITY In open pit mining, the economic necessity of keeping waste rock removal to a minimum generally means that the mine slopes have to be excavated to the steepest possible slope angle. On the other hand, excessive steepening of these slopes can induce failures, which may negate the economic benefits that have been aimed at and which may also result in loss of life and damage to equipment. Consequently, where slope failures are likely to prove to be a problem, an evaluation of the stability of the slopes to be created should be included as part of the overall pit design. How is the stability of a rock slope evaluated? When this question was examined, during discussions on the research policy to be followed at the Royal School of Mines, it was clear that relatively few satisfactory techniques were available in a form that would be comprehensible and therefore useful to the practical mining engineer. It was recognised that the research project must be directed towards two distinct aims: a) The evaluation of existing techniques for rock slope stability analysis and the provision of new techniques where these existing methods were found to be inadequate and b) The presentation of the results of this evaluation and research in a form that would be useful to engineers without specialist training in rock mechanics. It was soon realized that a university based research team, however large and efficient, could not achieve these aims without the co-operation and assistance of mining engineers,

Jan 1, 1972

By Rztssell H. Bennett

A SURVEY of the Mesabi Range iron-ore industry demonstrates that a satisfactory degree of technical progress has been achieved in the last fifteen years. This advance has not been made over a uniform front, but, by salients and bays, according to the different initial positions, economic and technical, of the component producing companies. The producers endowed with rich ore have in general, because of natural advantages, progressed more slowly than their neighbors with leaner properties. The advance has been made step by step all along the line -blasting, loading, hauling and concentrating-and without the benefit of radical innovation. There have been, for instance, no such parallel discoveries in iron ore as leaching and flotation in copper. The much lower unit price of iron operates, of course, to bar the application of these and other practices developed for the higher-priced metals. There exists, however, a radically new concentration process whose technology is well worked out and which may become economically operative in the not too distant future; this, as so often happens in engineering advance, because of recent developments in an entirely unrelated field. First, however, let me devote a paragraph or two to the more important economies effected in mining.

Jan 1, 1932

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is 'uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b'e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970