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By H. G. Moulton

The increasing scale of mining operations over the past decade, particularly in connection with the exploitation of large bodies of comparatively low-grade copper ores, has made necessary the study of the behavior of rock under failure. When extractions of as high as 40,000 tons a day are reached in steam-shovel operations and as high as 20,000 tons per day in underground mining operations, it is evident that excavations soon become of such size that the behavior of the rock will often be dependent on fundamental principles applicable to more or less homogeneous materials under stress, rather than on weathering or local planes of weakness. In the ordinary rock excavations encountered in civil-engineering practice, such as excavations for subways, highways, railroads, etc., rock faces are not carried to depths sufficient to develop any pressures, or consequently any failures, except those due to loose masses resulting from local planes of weakness. When, however, orebodies whose tonnage is measured by hundreds of thousands are to be extracted by steam-shovel operations in open pits, it is necessary to determine if possible in advance the slopes that the sides of the pits will assume, for these slopes influence the shape of the excavations and thereby the amount of ore that may be extracted by the open-pit method. When large orebodies are mined underground at depths of 300 to 500 ft. (91 to 152 m.) by caving methods, the surface subsiding as the ore is withdrawn, it is necessary to determine in advance the outermost limits of fracture in the subsiding surface, for on the delineation of these limits depends the location of surface improvements, mills, smelters, etc. and also the location of development work, such as hoisting shafts, main haulage levels, and all other underground openings that must remain undisturbed during the period of ore extraction. Heretofore, in civil-engineering practice, it has been assumed that earth and rock behave differently in failure. For the calculation of earth pressures, formulas are used in which the assumption is made that earth banks fail by sliding along the slope determined by the frictional resistance of the material. The line of failure and the resulting pressure is held to be dependent on the angle of repose, which is different for varying

Jan 1, 1920

By Butters S. E, Deslandes J. V

The selection of loading and haulage equipment in a proposed or oper- ating mine is vital in ensuring the cost effective achievement of produc- tion targets. To assist in the evaluation of different haulage systems, a truck haulage simulation model has been developed at BHP Melbourne Research Laboratories. The operation of the model is described and exam- ples of an actual application at Mt. Whaleback Mine is presented.

Jan 1, 1989

The Australian bulk explosives industry has matured significantly over the last five years and it would appear that the rest of the world is following suit. This maturity is characterised by the technical sophistication of modem bulk explosives, an increase in the technical competence of the explosives consumer and a greater openness in the debate on the quality and performance of explosives. The principal mechanism by which these advances have been made is undoubtedly commercial competition in the market place although a new element, technical competition between manufacturers and independent professionals, has and will continue to play an important role in the development of the industry. The relationship between the explosives manufacturer and consumer is necessarily both complementary and competitive. This paper identifies the need for the consumer to take a more prominent role in the critical analysis of the performance of explosives and to use his commercial influence to direct explosives manufacturers at least in the direction required for the future technical development of the industry.

Jan 1, 1990

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By A S. M A Haseeb

Zircon is the second in abundance among the heavy minerals occurring in the beach sand along the coastal belt of Bangladesh. In this study a detailed characterisation of Bangladesh zircon extracted at the pilot plant of the Bangladesh Atomic Energy Commission at CoxÆs Bazar has been attempted using chemical analysis, X-ray diffraction and optical microscopy. From the chemical analysis it is found that Bangladesh zircon has a purity of 95.88 per cent. The main impurity in Bangladesh zircon is titanium oxide (3.01 per cent). This is followed by iron oxide (0.42 per cent). A number of other oxides are also found. Microscopic study revealed that Bangladesh zircon has an elongated, prismatic shape with pyramidal termination in about half of the grains while the rest are more or less rounded. Some fractured and irregular grains are also found. Bulk sample of Bangladesh zircon in the as-received condition shows a yellowish brown color. However, individual zircon grains are seen to be almost colourless and transparent under polarised light. XRD study confirmed good crystallinity in the sample. Under the microscope it is found that zircon grains constitute 94 per cent while total impurities amount to six per cent in Bangladesh zircon. This result agrees fairly well with the chemical analysis results. Microscopic study identifies oxides of titanium (both rutile and ilmenite) to be the main impurity, in conformity with the findings of chemical analysis. Further, monazite was also identified as an impurity under the microscope. An iron bearing coating is also found on a few zircon grains. Most of the impurities found in Bangladesh zircon exist as discrete minerals.

Jan 1, 2000

By S. Henley

There is much in common between the requirements of open-pit mining and quarrying operations. Both involve the extraction of large volumes of material from surface excavations. The principal differences are of degree: open-pit mining of materials such as coal or gold generally involves the extraction of only small volumes of 'mineral' and large volumes of waste-they are operations with very high stripping ratios, and are made viable only because of the high unit value of the extracted mineral. In quarrying operations, the unit value of the mineral - sand, aggregate, limestone, or clay - is much lower, but stripping ration Are also lower. Thus the same techniques of geological modelling, reserve estimation, and pit planning are applicable, as is shown in two examples from the British quarrying industry. In each case, a primary requirement is the definition of production volume or tonnage. Sometimes, this need may be addressed simply by the use of a survey data processing package. However, in other cases, such as the two examples addressed in this paper, of sand and clay quarries, detailed assessment of the variation of mineral grades is a vital part of the exercise, and simple volumetric modelling cannot in itself be sufficient. In these cases, a block model approach using simple logical and numerical post-processing is also required to obtain required parameters for commercial classification of the products to be extracted. Pit designs themselves may be optimised by use of algorithms such as Lerchs-Grossmann, but the value of mineral produced can be dependent on factors other than its grade in any one part of a single pit, and the 'optimised' pit itself must be considered only a good sub-optimal. Given the right degree of healthy skepticism, and a software package with sufficient flexibility to be adapted readily to the rather different requirements of the quarrying industry, there is no reason why the quarrying industry should not benefit from the many years of investment in mining software technology.

Jan 1, 1989

By John A. S. Green, J. Gilbert Kaufman, Subodh K. Das

"The aluminum industry is a leading proponent of global sustainability and strongly advocates the use of recycled metal. As the North American primary aluminum industry continues to move offshore to other geographic areas, such as Iceland and the Middle East, where energy is more readily available at lower cost, the importance of the secondary (i.e., recycled metal) market in the U.S. will continue to increase. In the past, the recycling industry had been synonymous with the collection of aluminum beverage cans. However, as the opportunities for aluminum recycling have multiplied in motor vehicles, building and construction, and aerospace, these market are getting additional scrutiny for optimization of recycling strategies.Accordingly, the secondary industry can now draw upon a much wider range of product forms and alloys for its raw material, but this in turn brings issues of alloy sorting, impurity content, and control as the material is remelted and recycled into new product forms. The purpose of this paper is to take an integrated, industry-wide approach to look at the recovery of material from demolished buildings, shredded automobiles, and aging aircraft, as well as from traditional cans and other rigid containers. Attempts will be made to assess how the different alloys used in these separate markets can be recycled in the most energy efficient manner.IntroductionIn his recent book “Aluminum Recycling”[1], Mark Schlesinger points out that in traditional extractive metallurgy, the raw material used to produce a metal is mined from the earth and then is separated from other gangue minerals and impurities. In aluminum recycling, however, the ore body consists of scrap metal found on the ground, rather than in it. He further notes that scrap comes with its own variety of gangue and impurities such as painted coatings, other metal attachments, and even dirt and other contaminants. So, while the recycling process still requires some refinement and expenditure of energy, the effort and energy involved is much less than traditional mining."

Jan 1, 2008

By W. A. Johnson, F. N. Rhines, W. A. Anderson

The rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish- able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1942

By W. A. Anderson, F. N. Rhines, W. A. Johnson

THE rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1941

By W. A. Anderson, F. N. Rhines, W. A. Johnson

The rate of the high-temperature oxidation of pure copper has been measured repeatedly by numerous investigators. It appears to be generally agreed: (I) that at constant temperature, after the initial stages of oxidation have been passed and the scale has attained a substantial depth, the film thickness increases in proportion to the square root of the time of oxidation; and (2) that for any given period of oxidation the logarithm of the square of the film thickness is proportional to the reciprocal of the absolute temperature of oxidation.' These relationships are explained upon the basis that the rate of diffusion of copper to the external surface of the film is the controlling factor in establishing the rate of growth. Extensive studies have been devoted also to the mechanism and rates of the early stages of oxidation. There is thus available a reasonably well established theory of the oxidation of pure copper upon which to construct an explanation of the more complex oxidation of copper alloys. Few general principles have as yet emerged from the chaos of observations that have been reported in the field of the oxidation of alloys.2 It is evident, however, that the copper alloys may be divided into two main groups, whose oxidation characteristics are distinguish- able. The first group, composed of the alloys with the noble metals, forms substantially pure copper oxide scales; the alloying element is concentrated within the residual metal, and sometimes particles of almost pure noble metal are found in the scales completely surrounded by copper oxide. In the second group, composed of the alloys of copper with the baser metals, the alloying element appears as an oxide in the scale, often in greater concentration than in the alloy itself and sometimes to the exclusion of copper oxide. The oxide scales of the latter class have been found to be made up of one, two, and sometimes more distinguishable layers of which the innermost is often metallic in character, composed of particles of the oxide of the alloying element embedded in essentially pure copper and known as the subscale or zone of internal oxidation. The need for a thorough quantitative study of these modes of oxidation is evident. Since it is apparent that several mechanisms must be cooperating to produce the complex oxide scales found on copper alloys, the analysis of the process into its several simple operations should prove instructive. Fortunately, it is possible experimentally to produce internal oxidation in the absence of an external scale; this permits the isolation and intensive study of one of the steps in the oxidation process. In the present research the rates of internal oxidation of an extensive series of dilute solid solution alloys of copper have been measured and a theory has been developed to predict the observed

Jan 1, 1942

By E. S. Machlin

The kinetics of vacuum distillation, vacuum-melt surface reactions, crucible-melt surface reactions and boiling are analytically investigated. No disagreement with experiment is obtained upon applying a rigid flow model to describe the behavior of the melt in the vicinity of reaction surfaces. The theory focuses attention upon measureable parameters rather than upon the adjustable parameter, stagnant layer thickness, associated with other theories. The rigid flow theory is thus capable of quantitative evaluation and experiments to achieve this evaluation are suggested. KINETICS, rather than thermodynamics, often determine the degree of refinement achieved in vacuum melting. There is little understanding, however, of the kinetic principles involved in vacuum refining. This paper represents an attempt to achieve this understanding. There are two reactions which need to be con- sidered. The first is the refining reaction. The second shall be called the polluting reaction. It is the reaction associated with the introduction of components of the crucible into the melt. The mechanisms of both reactions are unknown. Many models can be constructed to describe either the refining or polluting reactions. For example, consider the refining reaction C + Q = CO(g). One model that can be imagined is that the carbon and oxygen combine in the melt to form CO which then diffuses to a melt-

Jan 1, 1961

By John Dilworth

THIS paper treats primarily of the valuation of developed coal properties by the method of capitalizing their estimated average future earnings. However, in it reference is also made to valuations of undeveloped coal lands and to various methods of appraisal other than by future earnings. FUNDAMENTAL VALUATION PRINCIPLES Before discussing in detail coal property valuations, a few statements bearing on the general subject will be made to present certain of the writer's views on the question as a whole. 1. A certain property at a given time has but, one true value. This is not universally admitted. The appraiser rather frequently finds that a coal owner has in mind three valuations for his holdings; one, the figure at which he feels they should be appraised for taxation purposes; another, the much higher one that should be used if a loan is to he negotiated on the property; and a third, intermediate between the other two, the price for which he would be willing to dispose of his holdings were they for sale. The last is usually nearest to the true value, and because this is so the statement is generally accepted that the fair value of such a property is the price arrived at by negotiation between a willing seller and a willing buyer who are otherwise disinterested. 2. Notwithstanding the foregoing, it is only very generally and approximately true that the proper measure of the value of a given developed1 coal acreage is the unit or per-acre price for which one or more bodies of similar coal in the salve district have been sold recently. To give a few reasons why such a measure of value can not be strictly applied, it may be noted:

Jan 1, 1927

IN this paper the author's intention is to convey a brief resume of the lead flotation treatment and lead flotation machines, which have replaced the May jigs and Wilfley tables at the plant of the North Broken Hill Ltd., and converted this mill into an all-flotation plant.Attention is directed to the fact that this drastic change from semi-gravity to all-flotation treatment, has been successfully accomplished without resorting to finer grinding than that previously in vogue for Wilfley table concentration, viz.: 10% to 16% plus 40-mesh I.M.M. screen.From the figures now available it is manifest that the scheme of all-flotation concentration-new as regards its successful application to Broken Hill ores is resulting in considerably higher-grade lead concentrates, and is substantially decreasing charges for labour, stores, and maintenance.The new treatment is far-reaching in its simplification of plant, as evidenced by the idle jigs and tables, and the results being obtained by North Broken Hill Ltd. may possibly influence metallurgical practice generally in Broken Hill.The outstanding features of the treatment are:(1) The coarseness, and high grade of lead concentrates obtainable.(2) The low time factor required for flotation.(3) The plant capacity, and the simplicity of its operation.(4) The low horse-power consumption.(5) The small cost for reagents used (not exceeding 3d. per ton of ore).

Jan 1, 1930

By P Murthy, Z Guan, P Townson

In this paper, we introduce a methodology to optimise mining equipment operation in terms of the conflicting concerns of productivity and availability. We also introduce the concept of damage points and equipment dutymeters. These provide the mine management with tools to monitor the success of such optimisation. Since we have quoted the results of an on-going Australian Coal Association Research Program (ACARP) project, the apparent focus of this article is on draglines. However, the concept is equally applicable to other equipment. Mining is the type of business that requires a large investment in capital infrastructure and equipment to produce a product that is sold at a relatively low unit cost. In such a business, the key to competitiveness lies in achieving the full realisation of capital investment ie sustained production at high levels. Some of the concepts outlined in this paper are essential components of this picture.

Jan 1, 2000

By John Sherbourne

Much valuable scientific research has been performed in recent years on the subject of phase behavior of hydrocarbons. ? 1-11 Engineers employed in petroleum production are interesting themselves in this work as well as in methods of applying the fundamental data available to the solution of their various problems. Recently a number of papers have been published in which applica-tions of phase behavior have been made to specific cases pertaining to critical phenomena.)12-16 Little effort, however, has been made in the literature to show the relation between changes occurring in the critical region and the more common phase behavior, therefore it is believed that a presentation of the fundamentals of phase behavior with reference to hydrocarbons is timely. Study of phase behavior is not new. In the metallurgical field, knowledge of heterogeneous equilibria has advanced tremendously, particularly with reference to solid-solid and solid-liquid behavior. Much is known about vapor-liquid equilibria too, but few engineers are familiar with this subject. ?

Jan 1, 1940

By Robert E. Campbell

Mining geophysics in 1969 marked a year of growth and consolidation in the application of ground and airborne geophysical methods and techniques with a 20% rise in expenditures for world-wide exploration. Growth was determined by questionnaire survey of industry, geophysical contractors, universities and government agencies conducted by the Society of Exploration Geophysicists. Relative position of metlhods is shown in the accompanying table on page 87. Methods and Techniques Electromagnetic airborne and ground methods showed the largest gains in the utilization of VLF-EM instrumentation. The VLF-EM instrument is a directional radio receiver which is tuned to distant radio transmitters in the 15 to 25 kilohertz band range. It measures vertical real and imaginary components of the magnetic field vector, and is used in geological mapping and surveying for various types of conductors in the ground. Ground VLF-EM instruments, Ronka EM-16 and Radem, are manufactured by Geonics, Ltd., Toronto, Ont., and Crone Geophysics. Ltd., Port Credit. Ont.

Jan 1, 1970

By Nelson Severinghaus

THE Rock Chapel plant of Consolidated Quarries Corporation (Fig, 1) is three miles northeast of Lithonia, DeKalb County, Georgia, It was opened about eight years ago for crushed stone aggregate. This paper reviews a number of experiments that have been tried in drilling and blasting, and gives the practice in use today. It also presents several theories on the action of explosives in this type of blasting. FIG, 1.-PLANT OF CONSOLIDATED QUARRIES CORPORATION, WITH QUARRY AT UPPER LEFT. The rock worked is a bare dome of granite gneiss about 3000 ft. in diameter, rising 150 ft. above the surrounding ground (Fig. 2). It is uniform in composition and quality, without seams, and extends down-ward to unknown depth below the quarry floor. A water well drilled 600 ft. remained in the same rock. The principal difficulty encountered in blasting is an easy split, which tends to break down the rock in large blocks.

Jan 1, 1938

By V. S. Rood

Typical System of Workings THE general system of workings at the Utah-Apex is similar to that found in many of the western metalliferous mines. There is a vertical three-compartment shaft extending to the surface, from which the various levels have been driven to the orebodies. The 1000-ft. (305-m.) level, about ¾ mile long, was driven as a haulage and drain adit. Geology The formation is a flat north-dipping series of alternating limestone and quartzite beds. Extensive north-south faulting and-fissuring have taken place, resulting in the formation of large replacement orebodies in the crushed zones in the limestone. The orebodies are irregular in shape and size, but follow closely the trend of the mineralizing fissures. The ore consists of galena, pyrite, sphalerite and small values in silver and gold. Large masses of non-commercial pyrite are frequently found in or adjacent' to the orebodies, and more or less pyrite is found for some distance in the walls of the orebodies. Lenticular bodies of a black pyritic shale also occur in the zones where extensive faulting has taken place.

Jan 6, 1918

By A. S. Odeh

This paper analyzes the effect of limited entry to flow at the wellbore on the steady-state productivity of a well. Wells that have been opened to flow along a fraction of their productive interval are termed wells with limited entry. Previous work treated the cases of a partially penetrating well, a well producing from the central portion of the productive interval and a well in which several intervals equally spaced were open to flow. In this paper the open interval can be located anywhere within the productive interval. Thus, in a sense, it generalizes previous work. The finite cosine transform was used to arrive at a solution for steady-state flow of a slightly compressible fluid. The solution was programmed for a CDC 1604 computer. Numerical vaIues for rd = 660 ft, r, = 1/4 ft, and range of sand thickness of 20 to 200 ft are presented in graphical form. The effect of rd and r, values on the result is shown in a table. The correct calculation of skin and damage ratio in the presence of limited entry to flow is explained and illustrated by examples. Moreover, the paper shows how to calculate the net decrease in productivity due to the combined effect of limited entry and perforations. INTRODUCTION In some wells only a fraction of the productive interval is open to flow. Location of this fraction is usually dictated by formation characteristics and reservoir behavior. For instance, if a gas cap exists, the open interval is located away from the gas-oil contact to prevent any possible gas coning. Wells that intentionally have been opened to flow along a fraction of their productive formation are tened wells with limited entry. Obviously, unintentional completions of this type also exist. Limited entry to flow decreases well productivity. Magnitude of the loss depends on the fraction of the formation open to flow, on the thickness of the sand, on the location of the open interval and on the ratio of rd /r, where r , is well radius and rd is the drainage radius of the well. The use of pressure buildup data on producing wells to calculate the condition of the formation around the wellbore is an accepted practice. van Everdingenl and Hurst2 introduced the concept of she skin factor s considered to be due to a thin layer of different permeability immediately around the wellbore. These authors dealt with the case of a well of complete radial geometry, i.e., a well with open-hole completion that completely penetrates the formation. The presence of a low-permeability skin results in a loss of productivity, as does limited entry. Therefore, if pressure buildup data obtained on a well with limited entry are used to establish the presence or absence of skin (i.e., formation damage), and a correction is not made for this loss of productivity, the calculations would result in an erroneous skin value. They might indicate the presence of formation damage when in reality there is none, or they might indicate a value larger than the true value. This could lead to an incorrect basis for planning remedial measures. Muskat3 studied the problem of partially penetrating wells for the case of incompressible flow. He presented equations and figures which allow estimation of loss in productivity. Brons and Marting,4 using equations based on Nisle's work,5 studied the loss of productivity for three cases. The first was for a partially penetrating well; the second was for a well producing from only the central portion of a productive interval; and the third was for a well in which several intervals equally spaced were open to flow. Their work was for steady-state depletion-type reservoirs wherein the well radius of drainage is established and the fluid is considered to be slightly compressible. Considered in this paper is the problem of wells with limited entry in which the open intervals are located anywhere within the productive sand. The finite cosine transform is used to arrive at a

Jan 1, 1969