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By J. E. Warren, J. H. Hartsock

Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, helve motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through. a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitcitions implied by the assumptions that were made, the following general conclusions were drawn. 1. For a radius of drainage at least four times us large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated. 2. The productivity of the hydraulically fractured system, relative to that of the unfructured well, can be determined from the apparent skin effect and can be used to establish design objectives. 3. In the evaluation of a fracture job, it is not Possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary. lNTRODUCTION Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years, it is only in the last few years that improvements in fracture design1-6 and fracturing technique' have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following. I. For a particular well in a given formation, what are the optimum design specifications for the fracture treatment? 2. Have the design objectives been achieved by the fracture treatment? The significance of these questions has been recoguized, and some attempts to obtain answers have been made. Howard, et al,8 endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy9 utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen10 to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al,11 attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner.12 These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should be sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments. Because this study is exploratory in nature, its scope

By W. A. Backofen, R. L. Fleischer

AN effect of orientation on the creep behavior of aluminum at 4.2 OK has been observed. Stress relaxation was measured in a hard-type tensile device after stopping the drive. From the spring constant of the device the load-time record could be converted to strain as a function of time. The strain sensitivity was 2-10-=, and the usual creep time of 1 min normally allowed a stress drop of about 25 g per sq mm. Further details of the apparatus and sample preparation appear elsewhere.' It should be noted that neither stress nor strain were constant, so that quantitative comparison with current creep theories will not be made. Shear strain (y) as a function of time (t) was consistent with logarithmic behavior: y = A In t, where A is a constant. In some cases t was made as large as lo3 sec. In the results the quantity A divided by t (the resolved shear stress, which is the driving force for creep) is plotted as a function of strain prior to creep. The quantity A/t is thought to indicate qualitatively the ease with which dislocations can move during creep. In Fig. 1 are drawn tensile stress-strain curves and A/T-strain measurements for single crystals of three orientations: l(a) and l(b) for the maximum resolved shear-stress orientation, l(c) for an orientation 2 deg from [211], and l(d) for a [111] stress axis. The following observations were made: 1) At low strains the A/t values are nearly the same for the three orientations. 2) As strains increase, A/t drops most rapidly for [Ill.] and less rapidly for [211], while for the maximum shear-stress orientation it is constant during easy glide and drops abruptly at the termination of easy glide. 3) In stage 11, A/t values are again approximately the same for the three orientations. These observations are regarded as evidence that 1) the initiation of slip produces obstacles of essentially the same effectiveness for all of these orientations, while 2) the rate at which slip obstacles are produced before stage I1 is fully developed is strongly controlled by the amount of slip on more than one system. This second statement is consis-

Jan 1, 1961

By Hugh Douglas

ANTIMONY Antimony (Sb) has been used since the early Egyptian dynasties. Prior to World War I, total demand amounted to only 6000 to 7000 tons per year (tpy). Wartime uses and rapid rise of industrialization in the Northern Hemisphere nations have pushed world antimony use to the 78,000-tpy level. An overwhelming supply of low-cost antimonial resources in the Sino-Russian bloc countries has and will continue to have a major impact on availability and price to users outside the bloc. Table 14.4.1 shows trends in world production, United States production and consumption, and prices. Demand Antimony is used principally as an alloy in lead-based metals and other alloys. Pure metallic antimony usage is small and is confined to such areas as laboratory and electronic applications. Lead-antimony alloys are used in automobile storage batteries, chemical pumps, and pipes, tank linings, roofing material, and cable sheaths. The metal increases the hardness of lead, and, for such uses as foundry printing type, reduces shrinkage for casting and lowers the melting point. Antimonial oxides are used for ceramic purposes, white paint pigments, glass forming, textile finishing, fire retardants in military clothing, matches, and solder. Wartime applications include use as hardener for bullets, an element for tracer bullets, and ingredient for producing dense white smoke for visual markers. A small but rapidly growing use for antimony is for metallic compounds in semiconductors and thermoelectric devices. In the United States demand for antimony is about evenly divided between metallic end-use markets and nonmetallic markets. In metallic end uses, antimonial lead accounts for 27% of total metallic and nonmetallic use; in nonmetallic areas major uses are flame retardants (15%) which is the fastest growing market, plastics (13 % ), and ceramics and glass (11%). While antimony has advantages in most of its applications, there are uses in which other materials can be substituted, including: mercury, titanium, lead, zinc, chromium, tin, and zirconium in paints and pigments; tin in sheathings; calcium in battery plates; and bismuth in type metal. Supply Antimony is produced from both antimony ores and as a byproduct of smelting other ores. The principal ore mineral is stibnite (Sb2S3), along with its oxidized antimonial minerals and derivatives which occur in small discontinuous replacement veins or fissure vein implacements. Stibnite occurs in quartz-gold veins and copper-lead-zinc

Jan 1, 1976

By J. P. Batcha, J. Robert Denny

Since 1964. Newmont Mining Corp. has been engaged in a systematic research and development of computer techniques for a variety of mine planning applications. The general objective of this effort has been twofold: first, to arrive at a viable near-optimum plan for mining a particular orebody and, second, to decrease the financial investment by reducing the man-hours required for mine planning. Three major phases in the evolution of Newmont's computer techniques for mine planning are discernible. In phase one, the computer's ability to duplicate manual drafting and contour mapping was developed. Obviously, all recognized geologic characteristics had to be included, and consequently the development of computer techniques for the proper incorporation of structure, stratigraphic trends, and other geological features was a significant aspect of phase one.

Jan 1, 1970

By E. S. Vargas, T. W. Chapman, Samuel W-S Tse

Models for interphase mass transfer rates in the solvent extraction of metals are developed for zinc and copper chlorides being extracted by trilsooctylamine and for copper extraction by LIX 64N from ammonia solution. The approach is to adopt a stagnant film model on which film thicknesses are known and to derive the interfacial metal fluxes for the case where all reversible reactions are fast and locally equilibrated. A growing drop mass transfer cell is used to measure extraction rates. It is found that for the cases studied the transfer rates are mass-transfer limited On the other hand, copper extraction by LIX from acidic solution exhibits slow reaction kinetics, and earlier kinetics models are confirmed. Interactions that cause varying selectivity in the simultaneous extraction of copper and zinc chlorides are demonstrated.

Jan 1, 1981

By F. P. Agterberg

It can be useful to model the mean grade values for a metal in mineral deposits containing that metal as representing the extreme value tail of a lognormal frequency distribution for the concentration values of the metal in common rocks of all types. Results for copper and zinc in the Abitibi area of the Canadian Shield are compared to results previously obtained for the Canadian Appalachian region. The lognormal model is also applied to a set of 162 large gold deposits in the Abitibi area. In the second part of the paper, 1311 large and small gold deposits in the Abitibi area are modeled as discrete events. By means of a newly developed spatial clustering model it is possible to predict the variances of random variables for frequencies of deposits in cells of different sizes.

Jan 1, 1981

By G. Ferrara

In process and plant simulation, more reliable prediction of industrial results and evaluation of data for designing purposes may be attained by the combined use of (a) modeling and simulation of ore characteristics and (b) modeling and simulation of integrated plant operations. The systems for modeling and simulation of ore characteristics are discussed as well as the conditions in which their use may be necessary (complex structure of the ore-body and variability of the ore fed to the plant). Two examples, for coal and bauxite run-of-mine (ROM), are reported. The procedure of linking the process unit models and the approaches for the solution of integrated systems are indicated. A general-purpose program for the simulation of integrated plant operations is described, and some examples of its use are reported.

Jan 1, 1984

By P. G. Dunn

Geologic studies during development at Copper Flat were directed at acquiring the necessary information in evaluating a low-grade porphyry copper deposit. In addition to the geologic mapping and core-logging of a typical exploration project, these studies included: - careful checks on the sampling and assaying, - selection of representative samples used to establish the recoverable amounts of precious metals in the ore, - examination of underground workings driven to provide samples both for metallurgical testing and for assay comparison, - evaluation of plant site and waste dump areas as non-material, including a placer examination of the tailings disposal area, and location of an adequate water supply. All these investigation were carefully documented to provide the necessary data both for the engineering design and, more importantly, for the feasibility studies required for successfully financing the project.

Jan 1, 1985

By Milton Ohring, Stephen M. Edelglass

THE recently determined coefficients for diffusion of very dilute impurities in aluminum are shown in Table I. Of these data the activation energies for Ag110, cu54, Mn54 and zn85 are clustered about the value of self-diffusion in aluminum; for the remaining

Jan 1, 1970

By V. M. Frey

IN 1936 the foreman at one of the oldest limestone quarries in northern Virginia discovered the remains of three old well-drill holes that contained dynamite. As consulting engineer for the property, I was then called upon to devise a method for removing the explosive. As no exact formula for the handling of unexploded dynamite exists, the proper steps for removing it must always be dictated by local conditions. A description of the procedure in this case may, therefore, be of interest to others faced with a similar problem.

Jan 1, 1939

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales: If members have copies of these volumes which they can spare, the price of $3 per volume will be paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will he given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will be sent and the balance will be credited to the payment of clues.

Jan 12, 1918

The necessary funds have been provided for the award in 1915 of three prizes, respectively of $50, $30, and $20, for the best essays, or other papers, submitted in competition by Junior Members and Members of Affiliated Student Societies. The following rules for the competition are therefore established in accordance with the instructions of the Board of Directors May 22, 1914: (1) A competitor for the President's Prizes must be, at the time of submitting his essay, either a Junior Member or a Member of an Affiliated Student Society of this Institute.

Jan 1, 1917

The Institute's stock of Volumes XXXI, LI, and LII has become much reduced by sales. If members have copies of these volumes which they can spare, the price of $3 per volume will he paid for them, if in good condition. If desired, a copy of the Index for Volumes XXXVI to LV will be given for one of these volumes of the Transactions and one dollar additional. For two volumes of the Transactions, a copy of the Index will he sent and the balance will be credited to the payment of dues.

Jan 1, 1919

By J. F. Harvard

We might say that for the metallurgist time "ambles withal," for the mining engineer time "trots withal," and for the geologist, time "gallops withal." And anyone for whom time "stands still withal" does not belong in the mining community today! In this bicentennial year of the United States of America we sense the mystery of time and we feel the pulse of history, especially in our own profession. What was mining like 200 years ago? What is it like today? What will it be like 200 years in the future?

Jan 7, 1976

By M. B. Truehaft

Expectations for coal in the early to mid-1970s prompted the government and industry to pursue research and development programs to increase underground and surface mining coal Productivity and net coal recovery. Several programs concerned advanced surface mining methods for thin seam coal recovery. Three such programs, along with related areas of interest, presented in this paper are: extended depth augering for trench-strip applications; high recovery auger heads for enhanced recovery; and variable wall mining in low cover longwalls. Conceptual development is examined, prototype testing is discussed, and potential operations are considered.

Jan 1, 1985

By Heinz W. Duddeck, Hans-Konstantin Nipp

The design of storage space or deep mining in rock salt should take into account not only time dependency of the rock salt behavior but also temperature effects. For deep mining of potassium salt the natural increase of temperature with depth may no longer be negligible. For the storage of cryogenic liquid gas in salt caverns more knowledge is nezded about the propagation of deep temperatures and their effects on the stress-strain-creep behavior of the surrounding salt. High temperature problems arise for nuclear waste storages in caverns or drill holes emitting radiation. A numerical model is proposed for the analysis of displacements and stresses including their time and temperature induced change. For the material behavior of salt constitutive equations are chosen composed of a combination of Hooke-Kelvin-Bingham-Newton-model based on experimental results (excluding at present deep cooling), Langer 1980. The parameters involved are depending on the stress level and the temperature. The finite-element-method is applied to rotationally symmetrical three-dimensional problems. The non-linear calculation method is based on an implicit method with respect to time. A modified Newton-Raphson-method and the initial strain approach are employed. Along with some experiences on suitable numerical procedures, examples are shown for the characteristical effects of time-temperature dependency. Having achieved convergency and reliability a method is now available for practical design and parametric sensibility studies.

Jan 1, 1982

By Charles Legrand

The problem of mine pumping is so much affected by local conditions, and those conditions are so liable to changes during the life of a mine, that the best system to use is difficult to determine. The experience of the writer has been that, in general, for copper mines, electric pumping is most satisfactory unless the quantity of water to be pumped is great or the mine does not use electric power for any other purpose. As a rule, however, figuring on the cost of necessary power plant, the total cost of installation is greater with electric pumps than steam pumps. As the water is liable to be gritty, outside-packed plunger pumps are to be recommended, and if the water is not acid, or only slightly so, chilled cast-iron plungers pay for their extra cost very quickly in diminished cost of packing. With chilled plungers it is possible to use metallic packing instead of soft packing, if the water is not too gritty or the lift too high. In vertical pumps this packing is satisfactory for lifts up to 400 ft., in the experience of the writer, and may be found satisfactory for higher lifts. For water slightly acid, cement-lined pump bodies have given good satisfaction. For acid water, both plungers and puhp bodies should be made of acid-resisting bronze. For high lifts, especially with gritty water, a satisfactory pump valve is difficult to find. To reduce the unbalanced pressure on the valve at time of opening it is advisable to have narrow seats; this, however, brings high pressures on the seats when the valve is closed. On large valves for lifts of 600 to 1,000 ft. we have used leather, hard rubber, vulcanized fiber, and soft brass; for clear water the latter has given best satisfaction. The difficulties due to grit make it advisable to have large sumps where water can settle, and if possible, to have two of them so that they can be cleaned alternately. At the mines of the Old Dominion Copper Mining & Smelting Co., Globe, it was found that a small air ejector discharging into a mine car provides a very convenient way to clean mud and sand from a sump.

Jan 1, 1916

By William B. Senseman

FOR reasons well known to mining engineers, wet grinding is quite universal in plants having to do with the extraction of metallic values from crude ores. In the processing of the nonmetallic and industrial minerals, dry grinding is the more common method. The crude materials usually contain less moisture than is required for wet grinding and the products usually are marketed in dry form; most of them as powders. To grind wet, therefore, would entail the addition of water and an expense for drying the product, which is not justified. Furthermore, the material would be a dried cake that would still have to be pulverized or disintegrated before use. For producing fine products, air separators have largely replaced the earlier practice of sizing with screens and bolting reels. Mills in which the air-separating feature is an integral part of the design are now commonplace. Mill designs are many and air systems have developed along various lines, but for the purpose of this discussion, only the fundamental idea need be emphasized the idea of using air for sizing and removing pulverized material from a grinding mill. About 20 years ago, when the use of mills equipped with air separation had become common practice, heated air or gas was introduced to such a system for the removal of moisture. The purpose of this discussion is to outline the developments and trends that have followed this experiment. It is an important development, for mills equipped with air separation are now universally used for pulverizing not only nonmetallic and industrial minerals, but a great variety of other materials. All such mills are essentially the same. Dried material is pulverized, removed by an air stream, trapped in a cyclone collector, and relatively clean air from the cyclone is returned through a fan to the mill. There is no theoretical need for a vent from the system. The practical need is to vent the air that leaks into the system, and, since the cyclone is not 100 per cent efficient as a dust collector, this vented air carries some dust with it. The initial attempt. at drying was made on a system like that described, by the addition of a furnace. The minus pressure within the mill draws hot gas from the furnace. Infiltration air, along with the drying gases and evaporated moisture, is vented as before. The first application was made to a mill used for pulverizing coal. The coal contained very little moisture, so very little drying effect was needed for the success of this experiment. Actually, some calculated efficiencies of over 100 per cent were obtained before due allowance was made for the conversion of mill power into useful heat. When moisture is low,, the heat obtained from the conversion of mill power is an appreciable part of that required. That drying can be effected in the short time interval available in a grinding mill of this type is better understood by visual-

Jan 1, 1945

By William B. Senseman

For reasons well known to mining engineers, wet grinding is quite universal in plants having to do with the extraction of metallic values from crude ores. In the processing of the nonmetallic and industrial minerals, dry grinding is the more common method. The crude materials usually contain less moisture than is required for wet grinding and the products usually are marketed in dry form; most of them as powders. To grind wet, therefore, would entail the addition of water and an expense for drying the product, which is not justified. Furthermore, the material would be a dried cake that would still have to be pulverized or disintegrated before use. For producing fine products, air separators have largely replaced the earlier practice of sizing with screens and bolting reels. Mills in which the air-separating feature is an integral part of the design are now commonplace. Mill designs are many and air systems have developed along various lines, but for the purpose of this discussion, only the fundamental idea need be emphasized— the idea of using air for sizing and removing pulverized material from a grinding mill. About 20 years ago, when the use of mills equipped with air separation had become common practice, heated air or gas was introduced to such a system for the removal of moisture. The purpose of this discussion is to outline the developments and trends that have followed this experiment. It is an important development, for mills equipped with air separation are now universally used for pulverizing not only nonmetallic and industrial minerals, but a great variety of other materials. All such mills are essentially the same. Dried material is pulverized, removed by an air stream, trapped in a cyclone collector, and relatively clean air from the cyclone is returned through a fan to the mill. There is no theoretical need for a vent from the system. The practical need is to vent the air that leaks into the system, and, since the cyclone is not 100 per cent efficient as a dust collector, this vented air carries some dust with it. The initial attempt at drying was made on a system like that described, by the addition of a furnace. The minus pressure within the mill draws hot gas from the furnace. Infiltration air, along with the drying gases and evaporated moisture, is vented as before. The first application was made to a mill used for pulverizing coal. The coal contained very little moisture, so very little drying effect was needed for the success of this experiment. Actually, some calculated efficiencies of over 100 per cent were obtained before due allowance was made for the conversion of mill power into useful heat. When moisture is low, the heat obtained from the conversion of mill power is an appreciable part of that required. That drying can be effected in the short time interval available in a grinding mill of this type is better understood by visual-

Jan 1, 1947

By William B. Senseman

For reasons well known to mining engineers, wet grinding is quite universal in plants having to do with the extraction of metallic values from crude ores. In the processing of the nonmetallic and industrial minerals, dry grinding is the more common method. The crude materials usually contain less moisture than is required for wet grinding and the products usually are marketed in dry form; most of them as powders. To grind wet, therefore, would entail the addition of water and an expense for drying the product, which is not justified. Furthermore, the material would be a dried cake that would still have to be pulverized or disintegrated before use. For producing fine products, air separators have largely replaced the earlier practice of sizing with screens and bolting reels. Mills in which the air-separating feature is an integral part of the design are now commonplace. Mill designs are many and air systems have developed along various lines, but for the purpose of this discussion, only the fundamental idea need be emphasized— the idea of using air for sizing and removing pulverized material from a grinding mill. About 20 years ago, when the use of mills equipped with air separation had become common practice, heated air or gas was introduced to such a system for the removal of moisture. The purpose of this discussion is to outline the developments and trends that have followed this experiment. It is an important development, for mills equipped with air separation are now universally used for pulverizing not only nonmetallic and industrial minerals, but a great variety of other materials. All such mills are essentially the same. Dried material is pulverized, removed by an air stream, trapped in a cyclone collector, and relatively clean air from the cyclone is returned through a fan to the mill. There is no theoretical need for a vent from the system. The practical need is to vent the air that leaks into the system, and, since the cyclone is not 100 per cent efficient as a dust collector, this vented air carries some dust with it. The initial attempt at drying was made on a system like that described, by the addition of a furnace. The minus pressure within the mill draws hot gas from the furnace. Infiltration air, along with the drying gases and evaporated moisture, is vented as before. The first application was made to a mill used for pulverizing coal. The coal contained very little moisture, so very little drying effect was needed for the success of this experiment. Actually, some calculated efficiencies of over 100 per cent were obtained before due allowance was made for the conversion of mill power into useful heat. When moisture is low, the heat obtained from the conversion of mill power is an appreciable part of that required. That drying can be effected in the short time interval available in a grinding mill of this type is better understood by visual-

Jan 1, 1947