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By Samuel G. Lasky

The writer has been interested in determining the mineralogic dis-t,ribut.ion of silver in the base-metal ore of thc Ground Hog mine of the Asarco Mining Co. in the Central mining district of New Mexico.' This ore consists of a varitextured mixture of sphalerite, chalcopyrite, galena and pyrite in a quartz gangue. The average ore contains 14 per cent of zinc, 9.5 per cent of lead, 5 per cent of copper, and 10 oz. of silver per ton. Generally it is accepted that the silver in ores of this type, in which no definite silver minerals can be recognized, is contained in the base-metal minerals. Published assays of pure mineral specimens from many districts show that each of the base-metal minerals contributes in some degree to the total silver content of the ores, and to determine the proportionate amount contributed by each mineral in any specific ore it has been the practice to assay selected specimens of each mineral, the purity of which has been determined microscopically. There being no such assays available for the Ground Hog ore, and it being impracticable to have enough of them made to give average results, the writer resorted to a mathematical attack upon composite assays of large quantities of ore and concentrates. Surprising results were obtained, and it is the threefold purpose of this paper to present these results, to describe the mathematical method used, and to point out the value of using this method even when assays of pure specimens are available. Value of the Mathematical Method The obvious way of attacking the problem would be to separate cleanly large quantities of ore into its component minerals and then to determine the average silver content of each mineral by assay of representative samples. Since an absolutely clean separation is not feasible, it has been the practice, as mentioned above, to assay pure specimens of the different minerals. No one will contend seriously that the silver content of a base-metal mineral is constant throughout any particular deposit, and it will

Jan 1, 1935

By E. J. Freeh, W. E. Horst, R. C. Kellner

A technique useful in the important area of process-model building is described. The procedure is illustrated in the development of a mathematical model to describe the unsteady-state process of batch ball-mill grinding. The influence of certain assumptions relative to model structure are quantitatively evaluated and reviewed.

Jan 1, 1969

By T&apos Ke, ing-sui

THE subject of recrystallization and grain growth has been much studied and the literature on this subject is numerous. Such studies have been mostly carried out by metallographic examination of X ray methods. Since recrystallization and grain growth involve elementary atomic processes, their mechanism can best be elucidated by a study of some properties which can be readily traced back in terms of such atomic processes. Prior to a detailed quantitative study, however, it is necessary to explore first the possibility and practicability of utilizing any particular property for obtaining the desired information. We have pointed out in a preceding article' that the internal friction of cold-worked metals is extremely high during recrystallization and it drops abru~tlv once the recrystallization is complete. ~reviois work has also shown that the viscosity of grain boundaries in a recrystallized specimen at a given temperature is raised by grain growth.' It seems thus that the measurements of internal friction may furnish a useful tool for the study of the mechanism of recrystallization and grain growth in terms of elementary atomic processes. The purpose of this paper is to report results of a study along this line. We will demonstrate that the internal friction method does give results in agreement with those furnished by conventional metallographic examinations. Once such a correlation has been established, we will be in a position to take further steps to achieve new information which cannot be achieved by conventional methods. The measurements of internal friction were made using apparatus and procedures similar to those used in the preceding article. All the measurements were made under such a small stress level that the internal friction is independent of stress level. The frequency of vibration is, unless mentioned otherwise, about one cycle per second in all cases. Internal Friction and Recrystallization Complete Recrystallization Temperature: Fig. 1 shows the internal friction curve during annealing of a few metals: aluminum, alpha brass and iron. These curves were determined in the following manner. In the curve for aluminum, internal friction measurements were performed upon. 99.991 aluminum subjected to 95 pct reduction area. The internal friction was first measured at room temperature. The specimen was then annealed at 50°C

Jan 1, 1951

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Jan 1, 1938

By J. R. Bridge, D. A. Vaughan

The phase diagram of the Zr-H system over the range 0 to 65 atomic pet was determined by high temperature X-ray diffraction methods. Results show a eutectoid between a zirconium and the hydride phase. The eutectoid temperature was established at 560±10°C with a eutectoid composition of 42*3 atomic pet H. The hydride phase of the lowest hydrogen content is stable only above the eutectoid temperature, but is formed and retained in a metastable state during reaction of zirconium with hydrogen at temperatures below 560°C. One hydride phase is indicated that exists over the composition range 55 to 65 atomic pet H. RECENT increase in the industrial importance of zirconium has stimulated several investigations of the reaction of zirconium with hydrogen. Review of the literature on interpretation of absorption isotherms' ' shows that attempts were made to relate the observations to the room temperature hydride phases reported by Hagg.3 However, more recently Schwartz and Mallett' reported the existence of a new hydride phase, isomorphous with the lower hydride in the Hf-H system described by Sidhu.4 This phase was found adjacent to the metal in a diffusion gradient sample. In addition to the new phase, Schwartz and Mallett reported on only two of the five hydrides found by Hagg. Gulbransen" confirmed the existence of only three hydrides of

Jan 1, 1957

By Georges Caraghiaur

INTRODUCTION A small, independent mining enterprise (SIME) is an independently owned and operated business concern engaged primarily in mineral development, from the exploration to the production stage. A SIME may or may not be listed on stock exchanges. By definition, a SIME is not dominant in its field and has no long-term financial backing. As such, it is not a major producer of minerals, nor is it a petroleum company, a government organization or a subsidiary of such organizations. The survival and growth of a SIME is most often controlled by an independently minded entrepreneur, who not only conceives and carries out new projects, but is materially affected by the success or failure of these projects. Usually, a SIME does not have a large or constant cash flow. Such a lack of long-term financial backing forces the SIME to meet the challenge of finding capital for its activities on a step-by-step basis. Its survival strategy is thus based on finding funds at the right time, of the right type and in the right quantities. The purpose of this paper is to show that the type of venture in which a SIME is involved affects the difficulty of raising new capital and the choice of possible sources of funds. The Small, Independent Mining Enterprise The SIME, also called small miner, junior mining company, speculative mining company, and pennystock mining company, is not a figment of the imagination of financial speculators. In Canada, there are more than 1,800 small mineral enterprises which spend on the average less than $1,000,000 per year on activity which is directed at bringing forth new mineral supply. In the United States, 64 percent of the non-fuel mining operations are conducted by nine or fewer men, and the coal industry is characterized by several thousand smaller independent producers, still predominantly family-owned or controlled. In Chile, 80 percent of the mines can be classified as small mines. In the Philipines, approximately 60 percent of metal mining operations are classified as small mines. The SIME is actively engaged in mining all over the world, and very much so in the Pacific Rim. The Mineral Supply Process The whole process of bringing forth new mineral supply involves a dynamic sequence of activities, ranging from the initial exploration for a mineral occurrence to the production of a marketable product. A typical sequence is outlined in Figure 1. At the grass-roots exploration stage, a series of geological, geophysical and geochemical tests is aimed at locating a mineral occurrence. Especially in the early phases of such activities, the uncertainty (risk) surrounding a venture is high, since only general geological information exists on which to base a judgement of the economic viability of the venture. Such risk is attractive to few investors.

Jan 1, 1982

By Carl W. Volz

NORWAY'S metallurgical development, which has extended over many centuries, is intimately associated with that country's unique topography and climatic conditions. It is a rugged mountainous country, with a most irregular shore line, bordered by thousands of islands forming a natural protection for shipping. There are an endless number of lakes, and innumerable rivers and waterfalls, many fed by glaciers and melting snow. Rainfall is abundant. Though half of the country is north of the Arctic Circle, it is warmed by the Gulf Stream, so that the average temperature is about 45°, or 20° higher than other parts of the world in the same latitude. A sub-

Jan 1, 1935

By N. S. Keith

Some time ago, a firm engaged largely in the manufacture of copper sulphate, applied to me for information as to the practicability of obtaining the copper from their mother liquors by means of electricity ; having reference, more especially, to obtaining the electric current from some magneto-electric or dynamo-electric machine. The mother liquors were the result of several solutions of commercial scrap copper, containing impurities, the quantity of which

Jan 1, 1879

By J. W. Fuller

DURING the last 20 years, experimenters have sought to utilize pulverized coal in boiler plants, but refractory and slag troubles have usually overbalanced any, gains in efficiency that were obtained. These troubles were caused largely by lack of knowledge of the proper methods of coal preparation and lack of a furnace design that would be adaptable to pulverized-coal firing. When this information was obtained the results were so much more satisfactory that within the last 5 years approximately, 80,000 boiler hp. have been installed in plants ranging from 1000 to 20,000 boiler hp. rated capacity, which are operating at an average of 174 per cent. of rating. The first commercial installation for burning pulverized coal under boilers was made at the Parsons shops of the M. K. & T. railroad in 1916. Of eight 250-hp. water-tube boilers thus fitted, six were operated continuously for 3 yr., when oil was obtained at such a low price as to warrant its use. Since then, this plant has been operating alternately on pulverized coal and oil, depending on prevailing prices. Recently gas has been discovered within 20 mi. of this plant, so that this fuel may also be used. No change in furnace design was made when changing from pulverized coal to oil or gas firing. One of the principal advantages of this method of firing is its ability to utilize, with maximum efficiency, all kinds of coal, irrespective of quality or physical characteristics. In fact, quite a number of the present pulverized-coal installations were made for the purpose of utilizing coal that could not be marketed or used in any other way. The Pacific, Coast Coal Co., at Black Diamond, Wash., formerly hand fired the boilers, using approximately 125 tons of prepared steam-size coal daily. The Black Diamond steam coal is the best quality of coal for steaming purposes mined in that section of the country, and there is a market for all that can be produced. By installing a pulverizing plant, it was possible to substitute coal of a size and quality that had no commercial value, so that 125 tons daily of the best steam coal formerly used at the mines is now marketed.

Jan 12, 1921

By Paul A. Bailly

Around 4500 B.C., the Pharaoh of Egypt ordered a military campaign to the Sinai Peninsula and the shores of the Red Sea, to search for copper deposits which Egypt needed for jewelry, vases and weapons.5 To my knowledge, this is the first recorded expedition aimed at the discovery of minerals. The diligent Egyptian soldier-prospectors made discoveries through visual detection and manual effort, the approach which has given us the bulk of our mines to date. In the Rio Tinto District of Spain where Roman miners followed the Phoenician traders, we find the first evidence of discovery of hidden ore bodies in the absence of mineralized outcrops. This is how Joralemon 13 describes these Roman discoveries to the southwest of the Rio Tinto hills, under the flat plain of Seville:

Jan 6, 1979

By Paul Giesecke

Since most modern metallurgical plants are operated continuously and on a large scale, successful operation at maximum efficiency demands that an accurate knowledge of the performance at each stage of the process be available at all times. Quantitative analyses provide the most practical process guides, and it is essential to have analytical procedures that combine accuracy and speed. In continuous plant operations, large losses may occur if the time interval between the development of trouble at any stage and its recognition and correction is great. Many metallurgical plants are using rapid colorimetric and spectrochemical methods of analyses for control purposes. So-called "color coppers" may be cited as an example of the colorimetric methods, in contrast with- the routine use of the ultraviolet spectrograph for the analysis of steels.42 By means of this more refined spectrochemical procedure, a complete quantitative analysis of the molten metal is obtained every few minutes. During the past two years the Physics Division and the Ore Dressing Laboratory of the American Cyanamid Company's Stamford Research Laboratories have collaborated in a study of the use of spectrochemical methods for the analysis of various metallurgical products. New methods have been developed, which have proved of practical value in plant operation. The following pages give a general review of the principles of spectrochemical methods and also the details of several specific analyses. Principles of Spectrochemical Analysis In general, it can be said that a visible light spectrochemical analysis can be performed for any ion or molecule that is naturally colored, or that can be made to react with another to produce a colored salt or complex. Whereas transmission measurements in the ultraviolet and infrared portions of the spectrum are most useful for the analysis of organic molecules, * visible light measurements are of particular value for metal salts. Such elements as copper, manganese, cobalt, nickel, iron, molybdenum, vanadium, chromium, phosphorus, mercury, zinc, lead, and a great many others, can now be determined with a high degree of sensitivity, accuracy and dispatch. From the simplest of qualitative determinations, color analyses have been improved to such an extent that, at the present time, through the use of recording spectrophotometers, hundreds of accurate quantitative analyses can be performed by a single analyst during an 8-hr. day after the standardization curves have been established for the ions to be determined.

Jan 1, 1947

By L. D. Anderson

WHEN, after years of troublous experiences in roasting sulfide ores with heavy dust and fume losses resulting from the equipment and methods first available, there appeared on the scene of metallurgy that revolutionary process known as sintering, it was felt that at last there had been found the ideal method for preparing sulfide ores for blastfurnace reduction. Not only were the sulfides roasted but also the fine oxidized ores were bound together with them in strong porous cellular masses which were in the best possible condition for reduction. With the experiences gained in the manipulation of the Huntington-Heberlein, Carmichael-Bradford, and Dwight & Lloyd processes there developed a refinement of detail which brought the whole plan of roasting by sintering to a high plane of perfection. But that metallurgy is never stationary is revealed by the fact that changes in milling practice, particularly the development of flotation, have introduced a new set of problems in sintering itself. Inasmuch as it is felt that these problems have not yet been solved in an entirely satisfactory manner this paper is written to record the present practice of the Salt Lake Valley smelters with the hope that there will be brought forth such discussios as may perhaps lead to still better practice. By far the greater proportion of the sulfides smelted today are flotation concentrates. Usually they are high grade, sometimes as high as 70 per cent. and more in lead. They are extremely fine, many mills grinding the ore so that from 60 to 80 per cent. will pass through screens of 200 mesh. The physical condition in which many of these concentrates reach the smelters is disconcerting to the metallurgists. Some are of about the consistency of putty. Others are of a sticky, slimy nature. Others again, dried to the limit, are veritable powders. Remembering that the down-draft sintering charge for the best results must be porous enough to let air be drawn through it reasonably well, must be thoroughly mixed, and must have some coarse material in it to segregate out and form a layer on the grates, it will be understood that the advent of this extremely fine material has made necessary still further elaboration in the equipment and processes of preparing sulfides for the blast furnaces,

Jan 1, 1929

By Paul Giesecke

Since most modern metallurgical plants are operated continuously and on a large scale, successful operation at maximum efficiency demands that an accurate knowledge of the performance at each stage of the process be available at all times. Quantitative analyses provide the most practical process guides, and it is essential to have analytical procedures that combine accuracy and speed. In continuous plant operations, large losses may occur if the time interval between the development of trouble at any stage and its recognition and correction is great. Many metallurgical plants are using rapid colorimetric and spectrochemical methods of analyses for control purposes. So-called "color coppers" may be cited as an example of the colorimetric methods, in contrast with- the routine use of the ultraviolet spectrograph for the analysis of steels.42 By means of this more refined spectrochemical procedure, a complete quantitative analysis of the molten metal is obtained every few minutes. During the past two years the Physics Division and the Ore Dressing Laboratory of the American Cyanamid Company's Stamford Research Laboratories have collaborated in a study of the use of spectrochemical methods for the analysis of various metallurgical products. New methods have been developed, which have proved of practical value in plant operation. The following pages give a general review of the principles of spectrochemical methods and also the details of several specific analyses. Principles of Spectrochemical Analysis In general, it can be said that a visible light spectrochemical analysis can be performed for any ion or molecule that is naturally colored, or that can be made to react with another to produce a colored salt or complex. Whereas transmission measurements in the ultraviolet and infrared portions of the spectrum are most useful for the analysis of organic molecules, * visible light measurements are of particular value for metal salts. Such elements as copper, manganese, cobalt, nickel, iron, molybdenum, vanadium, chromium, phosphorus, mercury, zinc, lead, and a great many others, can now be determined with a high degree of sensitivity, accuracy and dispatch. From the simplest of qualitative determinations, color analyses have been improved to such an extent that, at the present time, through the use of recording spectrophotometers, hundreds of accurate quantitative analyses can be performed by a single analyst during an 8-hr. day after the standardization curves have been established for the ions to be determined.

Jan 1, 1947

By Galen H. Clevenger

Equipment for treating lead ores was added in 1905 to a copper plant which the United States Smelting Refining and Mining Co. had built in 1902 at Midvale, Utah, about 12 miles to the south of Salt Lake City. By 1906 the lead section of the plant had been rounded out and consisted of a 90-ton gravity concentrator, fifteen hand-rabbled reverbera-tory roasting furnaces, six blast furnaces, a briquetting plant for handling flue dust and fine ores, a regulus furnace for concentrating the low-grade matte made in the blast furnaces, and a baghouse. The copper section was later abandoned and the plant has been operated for many years exclusively as a lead smelter. Some 45 years had elapsed at the time this plant was built since the first attempts to smelt lead ores in the West, and lead smelting had become a large and profitable industry but fundamentally little that was really new had been developed, which could be embodied in a plant built in this period. Principles and tools to work with had remained much the same as those borrowed earlier from European practice. Capacities had been increased and there were mechanical improvements but hand charging was still in vogue and there was little attempt to recover suspended particles carried out with the furnace gases, beyond settling in flues, which usually was only partly effective for recovery of the coarser particles. Satisfactory roasting and preparation of the fine components of the charge were still partially solved problems. The Midvale plant of 1906 may be regarded as more or less typical of the smelting plant of this period for treating complex western lead ores as distinguished from the recovery of lead from the simple lead ores to the eastward. The operation of a concentrating mill directly in conjunction with a lead smelter was, however, not common practice. The ores treated in this plant have from the beginning come from mines owned and operated by the company or have been custom ores purchased in the territory tributary to the plant. The treatment of custom ores is an important service to the small producer who does not have sufficient tonnage to warrant a plant, and serves to increase the tonnage of the operator of large properties, thereby helping to reduce

Jan 1, 1937

By R. A. Greenkorn

This project originated in a practical problem—we needed five tracers that could be used together to locate flow paths in a pilot flood. While tracers for subsurface liquids have been used since the turn of the century,1-15 none of those reported in the literature appeared to be either consistent or quantitative enough for our purposes. Most were used in field systems without controlled experiments to determine the accuracy and precision of analysis, and many were tracers that could not be used collectively. The ideal tracer, of course, would follow the fiuid of interest exactly, traveling at the same velocity as the fluid front. But the ideal is impractical to attain because adsorption-desorption effects cause the tracer to lag behind the front; these effects, plus diffusion-dispersion effects, cause the tracer front to spread more than the fluid front. Thus, our objective was not to locate a tracer that would be ideal for all circumstances but rather, to find one that would approximately follow the fluid, or one that under controlled conditions could be corrected to calculate the movement of the fluid front. We considered tracers satisfactory—(1) if they were easy to analyze; (2) if their breakthrough-elution curves were not too different from those for the chloride ion, a tracer believed to follow the fluid front closely; and (3) if we could calculate from the curves a material balance, at 1.25-PV (pore volume) injected, within 5 per cent of that calculated from chloride curves. Of a possible 35 materials, we selected 13 tracers that could be quickly and easily identified and whose analysis was claimed to be accurate within 5 per cent. Only one of these, tritiated water, was a radioactive tracer. Radioactive tracers are easy to detect even in small quantities, but they require special handling and special equipment. Also, those that can be used together are limited because special equipment is required to separate emissions from the various tracers. Two of the original 13 tracers were eliminated in static tests to determine how accurately and precisely they could be analyzed, and to check on gross adsorption. The remaining 11 were flowed through a 9-ft linear sandstone model, and breakthrough-elution curves were obtained. Finally, three tracers were field-tested as breakthrough tracers. These tests are described in the following sections. The 13 tracers considered in these experiments were EDTA (ethylene diamine tetra acetic acid), fluo-rescein, picric acid, salicylic acid and ammonium, boron (as borate), bromide, dichromate, iodide, nitrate and thiocyanate ions, plus chloride ion and tritiated water. All but the chloride ion and tritiated water were subjected to static sand tests to eliminate the tracers that could not be analyzed quickly and accurately and to eliminate those that showed excessive adsorption. All but two of the tracers, EDTA and salicylic acid, qualified for flow tests on this basis. The procedures used in the static tests (see Appendix A for analytical details) were as follows. Each tracer (in the amount shown in Table 1) was dissolved in 1,000 ml of water. Then, 800 ml of this solution was added to 500 gm of sand, and the remaining 200 ml was reserved as a control standard. The sand-tracer mixture was agitated once a day over a 10-week period, and during this period we analyzed five duplicate samples from this mixture, along with five duplicate samples from the control solution. From the control-sample analyses, we constructed a control chart on which the sand-tracer analysis results were plotted. The control chart, and its use to determine accuracy and precision of analytical results, as well as the amount of adsorption, is described in Appendix B. The results of the static tests are summarized in Table 1, which lists the concentration c (concentration at time t) divided by c, (initial concentration). If there was no adsorption, c/c, = 1. The acceptable deviation from this value varied from tracer to tracer, depending upon the limits of analytical precision established for the different tracers. The best results were obtained with boron, bromide and dichromate, with all values falling within limits of accuracy and precision. Ammonium, iodide, nitrate and picric acid also were satisfactory, although the ammonium results were erratic. Flourescein and thiocyanate were unsatisfactory ini-

By H. H. Evinger, M. Muskat

A methoD of calculating productivity factors for oil, gas, and water systems in the steady state is presented as an illustration of the quantitative application of the fundamental data on the flow properties of heterogeneous fluid systems. While the numerical results of the calculations cannot be applied directly to field conditions, because they are based on permea-bility data for unconsolidated sands and involve specific assumptions regarding the nature of the reservoir fluids, the methods of analysis and interpretation should havc significance in considering certain specific field situations when the necessary field and laboratory data become available. Moreover, it is felt that even under the idealized conditions to which the numerical calculations refer they should serve to give at least the orders of magnitude of the effects of gas-oil ratio and connate water on observed productivity factors. Within the indicated limitations, the computations imply that the foregoing factors can explain only a part of the apparent discrepancy between the homogeneous fluid productivity factors and those obtained recently in field measurements on the West Coast. IntroductioN Sufficient laboratory research has been carried out in the last several years on the fundamental features of the flow of heterogeneous fluids through porous media to call for consideration of what can be done with this type of information. It has, of course, already led to a, much clearer general understanding of the mechanics of oil production. However, examples of the quantitative application of the results of such laboratory studies are few in the literature. part of the explanation for this fact lies undoubtedly in the lack of sufficient laboratory data relating to practical fluids and sand systems such as would occur ill actual oil reservoirs. However, unless it can be shown that if such data were obtained quantitative applications could be made, serious doubt may be cast upon the desirability of carrying on further extensive experimental research work on fluid flow. The purpose of this paper is to present one approach to the problem of quantitative application of laboratory data to practical field problems. Because the published results on the basic experiments with three-phase fluid systems in porous media are limited entirely to uncon-solidated sands, the numerical applications made here will not pertain directly to any actual field situation. However, they should serve to illustrate what could be done with fundamental laboratory data if they were extended to cover the field of consolidated sands. From this point of view, it is hoped it will serve to encourage further laboratory research on this problem. The particular application to be treated here relates to the calculation of the productivity factors for oil-gas-water systems in the steady state. This specific problem seems especially appropriate for discussion in view of the recent publication by Johnston1 of the results of produc-

Jan 1, 1942

By Thomas H. Sheldon

In the zeal for opening up new ore-bodies, or for extracting the ore from attractive bodies already opened up, we very often lose sight of the fact, that, after all, the operation of a mine is a business proposition, pure and simple, and, for the best working-results, should be treated upon a strict business basis. Of course, in every mine of consequence, a record is kept of expenditures and receipts, and such glittering generalities as " gross receipts," " net receipts," " mining expenses," and a per cent. profit," can be told to the cent; but does this record show economy of management, as compared either with the same record of other months, or with the record of other mines of the same class ? Moreover, if such a record shows that the cost of mining is high, does it in any way enable the manager to put his finger on the leakage ? Does it necessarily follow that a mine which makes a profit of, say, 40 per cent. on 25-dollar ore, is doing less economical mining than one which saves 60 per cent. on 80-dollar ore ? Of course the figures in the latter case look the more attractive; yet when it comes to the point of saving everything which can be saved, and of cutting down expenses to the lowest possible cost of operation, the former mine is doubtless on the firmer and more economical financial basis. But as to the relative merits of the system of mining in the two cases, nothing could be decided without a basis of detailed comparison ; if one system is more economical than the other, why is it so, and wherein does the advantage lie ? This can be shown only by keeping accurately the cost of each mining operation. And no matter how dissimilar two mines may be in character and operation, yet there are a few general heads common to all mining operations. In the first place, it is necessary to break the ore from the solid ground;

Jan 1, 1907

By M. Muskat, H. H. Evinger

A methoD of calculating productivity factors for oil, gas, and water systems in the steady state is presented as an illustration of the quantitative application of the fundamental data on the flow properties of heterogeneous fluid systems. While the numerical results of the calculations cannot be applied directly to field conditions, because they are based on permea-bility data for unconsolidated sands and involve specific assumptions regarding the nature of the reservoir fluids, the methods of analysis and interpretation should havc significance in considering certain specific field situations when the necessary field and laboratory data become available. Moreover, it is felt that even under the idealized conditions to which the numerical calculations refer they should serve to give at least the orders of magnitude of the effects of gas-oil ratio and connate water on observed productivity factors. Within the indicated limitations, the computations imply that the foregoing factors can explain only a part of the apparent discrepancy between the homogeneous fluid productivity factors and those obtained recently in field measurements on the West Coast. IntroductioN Sufficient laboratory research has been carried out in the last several years on the fundamental features of the flow of heterogeneous fluids through porous media to call for consideration of what can be done with this type of information. It has, of course, already led to a, much clearer general understanding of the mechanics of oil production. However, examples of the quantitative application of the results of such laboratory studies are few in the literature. part of the explanation for this fact lies undoubtedly in the lack of sufficient laboratory data relating to practical fluids and sand systems such as would occur ill actual oil reservoirs. However, unless it can be shown that if such data were obtained quantitative applications could be made, serious doubt may be cast upon the desirability of carrying on further extensive experimental research work on fluid flow. The purpose of this paper is to present one approach to the problem of quantitative application of laboratory data to practical field problems. Because the published results on the basic experiments with three-phase fluid systems in porous media are limited entirely to uncon-solidated sands, the numerical applications made here will not pertain directly to any actual field situation. However, they should serve to illustrate what could be done with fundamental laboratory data if they were extended to cover the field of consolidated sands. From this point of view, it is hoped it will serve to encourage further laboratory research on this problem. The particular application to be treated here relates to the calculation of the productivity factors for oil-gas-water systems in the steady state. This specific problem seems especially appropriate for discussion in view of the recent publication by Johnston1 of the results of produc-

Jan 1, 1942

By James Norman

DIATOMACEOUS earth occurs in deposits widely distributed throughout the nation. The chief producing areas are in the Western States, where many high-grade deposits are known. Eastern deposits of diatomite are unsatisfactory for many purposes either because of impurity or because of the extremely fine particle size. Eastern users of diatomite, on the whole, must pay for transportation of the material from the west coast. The freight rate is necessarily high because of the great bulk of the diatomite. A satisfactory process of purifying the diatomaceous earths of Maryland and Virginia, which are unsuited for wide use only because of impurities, should be of value to eastern users. In the past, benefication of diatomite by wet processes has been limited to classification or sedimentation for the removal of sand from diatoms. Calcination with salt is used to produce a white diatomite when iron is present in the impurities, and small amounts of clay are rendered inactive in the process. No treatment has been developed whereby a large proportion of clay can be removed from a low-grade diatomaceous earth to give a diatomite of very high purity. In August 1937 the Federal Bureau of Mines, in cooperation with Dr. R. C. Williams, of Baltimore, undertook the problem of purifying low-grade Maryland diatomite by froth flotation. Work was done at the Eastern Experiment Station, College Park. Unless otherwise stated, the crude diatomite used was from the Patuxent River deposits near Dunkirk. This material, consisting of roughly one-third each of clay, quartz sand and diatoms, was representative of the usual low-grade marine diatomite found in the Coastal Plain Miocene beds of Maryland and Virginia and sporadically in other Atlantic coast states. As received, it contained 50 to 60 per cent moisture and probably had been wet since its formation.

Jan 1, 1940

By S. G. Gibbs

A new method for predicting the behavior of sucker-rod pumping systems is presented. The pumping system is described by a flexible mathematical model which is solved by means of partial diflerence equations with the aid of computers. Polished rod and intermediate-depth dynamometer cards can be calculated for various bottom-hole pump conditions. The technique permits simulation of a wide variety of operating conditions, both normal and abnormal. The data generated with the new technique are useful in refining the criteria for design and operation of sucker-rod systms. INTRODUCTION Sucker-rod pumping systems are used in approximately 90 per cent of artificially lifted wells. In view of this wide application, it behooves the industry to have a fundamental understanding of the sucker-rod pumping process. Oddly enough, our understanding has been rather superficial. This is evidenced by the semi-empirical formulas which have been used as the basis for design and operation of sucker-rod installations. Thoueh- we have realized the limitations of our methods for many years, it has not been computationally feasible to use more refined techniques. With the advent and widespread use of digital computers, it is now possible to handle the mathematical problems associated with sucker-rod pumping. This paper summarizes a computer-oriented method which can provide greater insight into the sucker-rod pumping process. It is hoped that this technique, and techniques which may evolve from it, will prove to be the tool needed by industry to obtain the most efficient use of rod pumping equipment. THE MATHEMATICAL MODEL Prediction of sucker-rod system behavior involves the solution of a boundary value problem. Such a problem includes a differential equation and a set of boundary conditions. For the sucker-rod problem, the wave equation is used, together with boundary conditions which describe the initial stress and velocity of the sucker rods, the motion of the polished rod and the operation of the down-hole pump. Of these items, the wave equation, the polished rod motion condition and the down-hole pump conditions are of primary importance. Discussion of the mathematical model centers about these factors. ROD STRING SIMULATION WITH THE WAVE EQUATION The one-dimensional wave equation with viscous damp- is used in the sucker-rod boundary value problem to simulate the behavior of the rod string. This equation describes the longitudinal vibrations in a long slender rod and, hence, is ideal for the sucker-rod application. Its use incorporates into the mathematical model the phenomenon of force wave reflection, which is an important characteristic of real systems. The viscous damping effect postulated in Eq. 1 yields good solutions, even though nonviscous effects such as coulcomb friction and hysteresis loss in the rod material are present. Fortunately, the nonviscous effects are relatively small, so the viscous damping approximation used in the wave equation is adequate. The coefficient v is a dimensionless damping factor which is found in field measurements to vary over fairly narrow limits. For mathematical convenience the gravity term is omitted in Eq. 1. The effect of gravity on rod load and stretch can be treated separately, as will be noted later. Since Eq. 1 is linear, the legitimacy of this procedure is easy to demonstrate. POLlSHED ROD MOTION SIMULATION The motion of the polished rod is determined by the geometry of the surface pumping unit and the torque-speed characteristics of its prime mover. By determining the motion of the polished rod, we formulate an important boundary condition. From trigonometrical considerations it can be shown that the position of the polished rod vs crank angle 0 is given by (see Fig. 1) These equations are obtained from the general solution of the "four-bar" linkage problem and can be used to describe the kinematics of any modern beam pumping unit.' If prime mover speed variations are disregarded, the angular velocity of the crank is constant, and Eq. 2 can be used to predict the position of the polished rod vs time. However, the constant-speed condition leading to constant crank angular velocity is only approached in practice: hence, it is better to make provisions for prime mover speed variations in the mathematical model. The speed at which the prime mover runs is determined by its torque-speed characteristics and the torque imposed upon it. The torque that the prime mover "feels" is the net torque arising from the polished rod load and the opposing torque from the counterbalance effect. The