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The Institute maintains a dual reltionship with students: (1) an individual relationship with a Student Associate; and (2) a relationship with local organizations of students, known as Affiliated Student Societies or Student Chapters. 1. The conditions of Student Associateship are set forth in Section 9, Article I, of the Bylaws of the Institute (see page 60 and following pages). During 1934, sundry amendments were made for the purpose of improving the student relationship. Post-graduate students are now eligible; and associateship can be maintained, with the payment of the regular dues of $2 per year, for 18 months following graduation in. June. With his regular dues, each Student Associate is entitled to receive during the year his choice of MINING AND METALLURGY, METALS TECHNOLOGY, MINING TECHNOLOGY, PETROLEUM TECHNOLOGY, or two "classes" of Technical Publications; and on payment of an additional fifty cents. he can have both MINING AND METALLURGY and any one of the others. He is accorded the privilege of getting special publications such as "The Porphyry Coppers" and "Elements of the Petroleum Industry" at the reduced prices applicable to Members; he has the privileges of the Engineering Societies Personnel Service and the Engineering Societies Library; and he is not only invited but urged to attend all meetings of the Institute, its Divisions and its Local Sections. The Institute wants, to extend the hand of professional fellowship to students following mineral industries curricula.

Jan 1, 1941

By Mark L. Requa

During the past two years California has developed a new and important oil-field: I refer to Midway. This field produced the famous Lake View gusher, which is credited with a total production in excess of 8,000,000 barrels. Fortunately for the oil industry of the State, this well is now a thing of the past, and nothing, save a great crater-like opening marks its location. The pipe is entirely worn away and gone; and it is a matter of serious doubt if there can be anything done that will cause the well to produce again. Fortunately, also, there have been no other wells in that field or elsewhere throughout the State that in any may compared with the Lake View. Midway is noted for large wells, of from 500 to 2,000 barrels production; but the decline is rapid, and a few months serve to bring the output down to a few hundred barrels. In the oil-territory heretofore blocked out as proved and probable, there have been, during the year, many changes. Some areas which were expected to be fairly productive have apparently failed; others, more strictly "wild-cat," have come in; while in some of the older fields there are properties which are beginning to shorn evident signs of exhaustion. The total area of proved territory will therefore probably suffer but small

Jan 1, 1912

By R. G. Fenish

THE B-Ni system was chosen for this study because of the great interest being shown in boron-fiber-strengthened composite materials. Boron fibers were obtained from Texaco Experiment, Inc. They average 4.2 mils in diam with a 0.5-mil tungsten wire in the center. In order to make the diffusion couple, the fibers were included in the nickel matrix by electroforming. The samples were placed in a preheated furnace for the desired temperature and length of time. Sectioning and polishing the samples revealed concentric rings as shown in Fig. 1. The average penetration distance, X, was calculated by measuring the radius of the second phase (the white shell in Fig. 1) and subtracting the original radius. The second phase was identified as NiB by X-ray diffraction. This allows the kinetics of the formation of the phase NiB to be calculated by Eq. [I], which is taken from Hoffman:"

Jan 1, 1967

By F. W. Rols-Hausen, F. W. Jessen

It is the purpose of this paper to present data on brines occurring in the Frio formation of the Texas Gulf Coast, and to show how their composition varies, (1) with depth below the surface, (2) with depth below the top of the formation, and (3) along the approximate strike. The brines vary in chloride content from 3,180 to 73,000 p.p.m., though the average salinity of the salt waters is shown to vary with total depth; the concentration being 35,000 to 40,000 p.p.m. at 3500 to 5500 ft., slightly less than 50,000 p.p.m. chloride at 5500 to 6500 ft. and average 38,000 to 40,000 below 6500 feet. From the analyses available, it appears that the highest concentration of salts occurs in the upper 300 ft. of the formation, while lower salinity is found with increasing depth below this point. The salt waters from wells in Starr County show less concentration of dissolved salts than in any other group of wells farther north along the strike. In all, 116 analyses from 63 fields and 14 wildcats, from depths ranging from 1300 to 11,400 ft. below the surface and from z to 3240 ft. below the top of the Frio, are recorded. Introduction Brines have been studied for many Years in an attempt to solve some of the geologic and production problems associated with the production of oil and gas. One practical application of study of . water analyses is the correlation of waters occurring above, in, or below the producing sand in the same field or throughout the same formation. The Frio formation, the series of sands and shales occurring below the Marginulina zone and above the Vicksburg, is one of the major oil and gas-producing formations in the Texas Gulf Coast. Fossils are rare or absent in the upper Frio throughout most of the area. When available, cuttings and cores, and electric logs were used to determine the top of the Frio. A change in lithology was used to determine this point in most of the wells, and fossils were used in some of the deep wells. It is realized that a change in lithology is not perfect for correlation purposes over long distances and some of the trends may be influenced by the inability to differentiate between the nonfossiliferous Marginulina zone and the Frio. It underlies virtually all the area shown on the accompanying map (Fig. I). Although it is not productive in the updip facies, it has been explored to a limited degree below I2,000 ft. Further more, toward the coast line future drilling to deeper depths should encounter this formation. Although thousands of wells have penetrated or drilled entirely through the formation, very few water samples have been secured from the many sands occurring in this formation and analyzed. Previous Investigation No previous published study has been made of the chemical composition and concentration of waters from the Frio formation. However, one water analysis

Jan 1, 1944

By F. W. Jessen, F. W. Rols-Hausen

It is the purpose of this paper to present data on brines occurring in the Frio formation of the Texas Gulf Coast, and to show how their composition varies, (1) with depth below the surface, (2) with depth below the top of the formation, and (3) along the approximate strike. The brines vary in chloride content from 3,180 to 73,000 p.p.m., though the average salinity of the salt waters is shown to vary with total depth; the concentration being 35,000 to 40,000 p.p.m. at 3500 to 5500 ft., slightly less than 50,000 p.p.m. chloride at 5500 to 6500 ft. and average 38,000 to 40,000 below 6500 feet. From the analyses available, it appears that the highest concentration of salts occurs in the upper 300 ft. of the formation, while lower salinity is found with increasing depth below this point. The salt waters from wells in Starr County show less concentration of dissolved salts than in any other group of wells farther north along the strike. In all, 116 analyses from 63 fields and 14 wildcats, from depths ranging from 1300 to 11,400 ft. below the surface and from z to 3240 ft. below the top of the Frio, are recorded. Introduction Brines have been studied for many Years in an attempt to solve some of the geologic and production problems associated with the production of oil and gas. One practical application of study of . water analyses is the correlation of waters occurring above, in, or below the producing sand in the same field or throughout the same formation. The Frio formation, the series of sands and shales occurring below the Marginulina zone and above the Vicksburg, is one of the major oil and gas-producing formations in the Texas Gulf Coast. Fossils are rare or absent in the upper Frio throughout most of the area. When available, cuttings and cores, and electric logs were used to determine the top of the Frio. A change in lithology was used to determine this point in most of the wells, and fossils were used in some of the deep wells. It is realized that a change in lithology is not perfect for correlation purposes over long distances and some of the trends may be influenced by the inability to differentiate between the nonfossiliferous Marginulina zone and the Frio. It underlies virtually all the area shown on the accompanying map (Fig. I). Although it is not productive in the updip facies, it has been explored to a limited degree below I2,000 ft. Further more, toward the coast line future drilling to deeper depths should encounter this formation. Although thousands of wells have penetrated or drilled entirely through the formation, very few water samples have been secured from the many sands occurring in this formation and analyzed. Previous Investigation No previous published study has been made of the chemical composition and concentration of waters from the Frio formation. However, one water analysis

Jan 1, 1944

By A. E. Jenkins, O. C. Roberts, D. G. C. Robertson

Using an inverted-cone coil at 450 kHz, it has been possible to levitate iron (FeS), cobalt (CoS), and nickel (NiS) sulfides. Important nontransition metal sulfides such as ZnS, PbS, and Cu2S have proven impossible to levitate although Cu-Fe-S ternary alloys containing 30 wt pct S and up to 10 wt pct Cu, and Cu-Co-S and Cu-Ni-S ternary alloys containing 30 wt pct Cu have been levitated. The levitation technique has been used in preliminary experiments on the vaporization from liquid sulfides and the reaction of liquid metal-sulfur alloys with oxidizing atmospheres. The course of the reactions with pure oxygen were followed using highspeed photography and two-color pyrometry. ELECTROMAGNETIC levitation is now established as a basic laboratory technique in high-temperature research but its application has been restricted mainly to metals and alloys. Applications have included alloy preparation,' metal purification,2'3 determination of liquid metal densities and emissivities,4,5 and studies of metal supercooling,4 alloy thermodynamics,6 and vaporization phenomena.7-9 The application of the technique to compounds has not been considered previously. The successful investigation of the reactions between dilute iron alloys and oxidizing atmospheres10'1 has prompted the current physico-chemical studies involving levitated metal sulfide drops and flowing inert or oxidizing atmospheres. This paper presents the results of such a study and provides a basis for future studies involving a wide range of other compounds of metallurgical interest. The successful levitation of many metal sulfides and mattes provides a method of studying the oxidation reactions fundamental to flash-smelting and similar pyrometallurgi-cal operations under closely controlled laboratory conditions. In addition the system allows the use of a controlled atmosphere (e.g., a gas stream of a certain H2/H2S ratio) with a particular chemical potential to study the relevant thermodynamic equilibria or the mass transfer processes between the atmosphere and the levitated drop under conditions where the hydrodynamics of the system can be closely defined. The optimum frequency for the levitation melting of metals in an inverted-cone coil type inductor is within the radio frequency range 400 to 500 kHz. At frequencies lower than 10 kHz the rate of heat generation is usually insufficient to melt the levitated charge' or where melting is achieved, "dripping" from the charge is encountered.'' At frequencies above 2 mHz the levitation force decreases. Metals, alloys and preheated elemental semiconductors such as germanium and silicon, have been levitated but the levitation of only a few metal compounds has been reported. Jostsons13 and the authors have levitated liquid titanium-oxygen alloys containing 50 at. pct 0 while clark14 has reported the levitation of mixtures of FeS and MnS for short periods. With a "cold crucible" inductor sterling15 has melted ferrites by preheating them by induction in a 4 mHz field and melting at a lower frequency. However this second type of inductor has been designed purely for the melting of materials without contamination; there is only a small gas film between the charge and the inductor and the electromagnetic levitation effect is of secondary importance. For this reason further discussion will be restricted to the use of the coil type inductor. The assessment of the suitability of a particular metal compound for levitation is based upon the following two criteria: i) thermal stability, and ii) physical "levitability". In this paper these two criteria will be considered separately. The thermal stability of a solid or liquid metal compound with respect to a gaseous environment depends upon its chemical reactivity with that environment or, in the case of an inert atmosphere considered here, its volatility. The physical criterion as to whether or not a particular compound can be levitated is based upon a comparison between those physical properties of the compound determining "levitability" which are defined by the fundamental equations of levitation theory as developed by Okress et a1.,16 and the properties of the metals. Since it is not practical to cover the vast field of metal compounds, further discussion will concentrate on the metal sulfides but the treatment would be applicable to any metal compound. THE THERMAL STABILITY OF METAL SULFIDES The temperatures usually encountered during levitation in inert atmospheres cover the range 1400" to 2000°C. The stabilities of the condensed states of the sulfides under these conditions are considered in relation to the periodic classification by reference to Table I. Two general classes of sulfides emerge. The solid sulfides of elements of group IIB and of groups further to the right are volatile while those sulfides of group IB and of groups further to the left are nonvolatile solids. The sulfides described as volatile may be dismissed as unsuitable for levitation. The stabilities of the more favorable nonvolatile sulfides under the anticipated conditions must be studied more closely From Table I it is seen that the alkali metal sulfides exist as liquids in the temperature range of in-

Jan 1, 1970

By Walter B. Lenhart

Introduction and Importance of the Industry Sand, as described in this chapter, is a crude product used for ballast on railroads and highways, and as the fine aggregate in concrete, mortar, plaster and in asphalt paving materials. The sand used in glass, as a molding sand, and as a source of silica is described in Chapter 43. Sand and gravel together constitute the mineral raw materials of largest volume produced from the earth. In 1958, as reported by the U.S. Bureau of Mines,21 680,080,000 tons of sand and gravel (including industrial sand) were produced in the United States. The nearest competitor was crushed rock of which 532,818,000 tons were produced. Coal, both bituminous and anthracite accounted for only 431,616,689 tons in the same year. In dollar value, sand and gravel were exceeded only by cement, crushed rock and fuels. Hence it is a major unit of the mineral-producing industry. As an example, one plant in California operates around the clock at an average rate of 1,500 tons per hour, and at peak intervals has shipped over 4,000 tons per hour, all by trucks. Nevertheless, it is controlled by one man through a panel of push buttons that control the crushing, screening, washing, grading, stock piling, and reclaiming of the products. Because sand and gravel are low-valued commodities, but are used in every construction undertaking in every city, village, farm, dam and highway, they are produced in almost every county in the United States and southern Canada, by thousands of individual operators, very few of whom operate in more than one community. Many operations, particularly those established to supply the needs of major dams that are under construction, or of major segments of new highways, are temporary in nature, and the equipment installed is more or less portable. Because of the bulky nature of sand and gravel, there is very little interstate movement, and almost no exports or imports, except a little movement back and forth across the border of the United States and Canada. First, the material needs definition. Definitions Sand and gravel have been defined as continuously graded unconsolidated materials that appear in the earth's surface as a result of the natural disintegration of rocks. Both normally appear together, but in a wide variety of sizes, types and range of size classification. The American Society for Testing Materials has tentatively revised its definition of "sand" as: granular material passing the 3/8-in. sieve and almost entirely passing the No. 4 (4760-micron) sieve and predominantly retained on the No. 200 (74-micron) sieve, and resulting from natural disintegration and abrasion of rock or processing of completely friable sandstone (ASTM Designation C 58-55T). The Society's tentative revision of its definition of "gravel" is: granular material predominantly retained on the No. 4 (4760-micron) sieve and resulting from natural disintegration and abrasion of rock or processing of weakly bound conglomerate (ASTM 125-55T). Sand and gravel deposits contain materials from the finest silt to the largest boulders. Chemical definition of the two materials is nearly impossible. Sand and gravel always are

Jan 1, 1960

Jan 1, 1881

By A. T. Janssen

Production planning of direct-shipping ore from a number of relatively small deposits serves to sequence development and mining of these deposits so that both long- and short-range demand can be met while the timing of development cost is such that the average annual rate is minimized. Hand-computed methods have the disadvantage that they require substantial effort and time and cannot be exhaustive. The application of operations research and computers not only overcomes these disadvantages, but opens up additional applications, such as feasibility studies involving alternative mining strategies and changes in the ore market. The method employed concerns linear programming and specifically the Big-M algorithm applied to the variant on the simplex technique with penalties applied to deviations from the desired ore grade. Acceptable 20-year production schedules could be generated in relatively little time, i. e. , in less than 200 seconds for the central processor of the Control Data Corporation 6400 system of the University of Colorado in Boulder.

Jan 1, 1969

By James E. Lonergan, Young C. Kim

Over the past two and one-half years, various emission control strategies for a coal-fired power plant have been jointly developed by the University of Arizona and the Homer City Owners. The objective of this work was to assist the Homer City management in their efforts to comply with SO2 emission regulations while continuing to use the relatively high sulfur coal from their captive mines as the primary source of plant fuel. One of the operational strategies studied was to have the captive mines minimize the sulfur variability of the run-of-mine coal on a short term basis. A mine production scheduling program called COMPF2 was developed to perform this task. This paper describes the application of this mine planning program at an underground coal mine. A comparison of the planning results with actual production figures showed the ability of this program to schedule production so as to minimize both the sulfur content and the sulfur variability of run-of-mine coal.

Jan 1, 1983

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Jan 1, 1938

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By Warren L. Howes

This paper deals primarily with an investigation of ball-mill liners that was conducted by the writer over a period of six years at the Mammoth mill in Arizona. The investigation covered a wide variety of designs of liners in both primary and secondary mills. The comparative results are presented herein as evidence of the extent to which design influenced liner life and mill performance. Flowsheet The feed to the Mammoth mill was a complex, oxidized, gold-silver-lead-molybde-num-vanadium ore with rhyolite, andesite and granite as gangue. Although the ore varied between stopes, the long-term average in character remained substantially the same. Capacity was 560 tons per day.† Fig. I shows an abbreviated flowsheet of the grinding section of the mill. Primary Ball Mill A 3-ft. Symons shorthead crusher in open circuit crushed to 1/4-in. maximum one-way dimension the feed to the 5 by Io-ft. Marcy open-end ball mill. The mill rotated at 80 per cent of critical speed and was charged with 4-in. forged steel balls. Cast balls were used for a few months at a slight reduction in ball cost, but breakage of the large balls reduced the ball size and grinding capacity to a point where the over-all costs suffered out of proportion to the saving in cost of balls. For metallurgical reasons, the finished product of the mill was maintained at minus 8-mesh. This coarse product, plus the very abrasive ore and the absence of fines in the feed, caused abnormally rapid wear of the mill liners. The resultant high operating cost led to the most extensive phase of the investigation. In order to clarify the difference in design of the various types of liners used, Fig. a shows the profiles with the arrangement in which grinding balls of maximum size would lie on the face of the liners. The results with each type of shell liner in the primary mill are shown in Table I. Since most of the testing was done with

Jan 1, 1943

By Alfred F. Brainerd

Some fifty years ago, iron-ore was discovered near the town of Sheldon, Franklin County, Vermont, in a vein out-cropping on a knoll near Black Creek, which empties into the Missisquoi River a couple of miles away. A short time after this discovery, the owners, Mr. TV. 0. Gadcomb and Hon. Lawrence Brainerd, both of St. Albans, commenced mining (mostly by open cut), and also erected a Catalan forge, from which iron blooms were produced, most of which were worked into bar-iron and used in the neighborhood of the forge, while some were shipped by Lake Champlain to Troy, Albany and New York. But by reason of the lack of any railroad connections, and an insufficient demand for the blooms, this forge was subsequently abandoned, and the material used in its construction removed to other places. Mr. Keith, of Sheldon, used for many years a mixture of this ore with bog-ore from Swanton, in a charcoal blast-furnace, the product of which he consumed partly in his own foundry, shipping, however, a considerable amount to Troy and New York. Accurate data as to this enterprise are not at hand. The same vein has since been traced for some 20 miles, and some prospecting has been done 011 its outcrops at Berkshire, Enosburg and a few miles east of St. Albans; but the vein being small, only a few car-loads of ore were taken out from these places. The commencement of the St. Albans Iron and Steel Works in 1872, and the erection in 1877 of a ten-ton Siemens open-hearth furnace for the manufacture of steel rails, opened a new use for this ore. The furnace-charge consisted of pig-iron, old mils, steel scrap, and magnetic iron ore, added towards the close of the heat. The ore

Jan 1, 1885

By E. Hoek

The stability of a rock structure depends primarily upon the extent to which fracture develops within the structure, The prediction of the extent of potential fracture, the first step in the study of fracture development, involves a knowledge of both the stress distribution in the structure and the criterion which governs rock fracture under various stress conditions. While a great deal of research effort has been devoted to the development of techniques for analyzing the stresses in mining and civil engineering structures1-3 and to the investigation of the fracture mechanism of rock 4-6 relatively little attention has been paid to the application of available knowledge to the solution of practical engineering problems. This paper describes a photoelastic technique for the determination of potential fracture zones in certain types of rock structures. A practical example, based upon a problem which might be encountered in designing the layout of deep-level mine excavations, is given as an illustration of the application of this technique. STRESS ANALYSIS AND ROCK FRACTURE In deciding upon the technique to be used for the solution of a problem involving the prediction of rock fracture it is necessary to consider: 1) What type of stress information is required to satisfy the fracture criterion for rock; anti 2) How this information can most conveniently be obtained. It has been established, both theoretically 4,7 and experimentally 5,6,8that the fracture of hard rock depends primarily upon the relationship between the algebraically greatest and the algebraically smallest of the

Jan 1, 1967

By Robert Schorr

PAGE 1. Introduction,........... 82 2. Characteristics of Briquettes,........ 87 3. The Manufacture of Coal- and Coke-Briquettes,.... 89 Binders, Organic and Inorganic,...... 90 Mixing,...........94 Presses, Continuous and Intermittent Action,....95 Cost of Briquettes and Sales-Prices in Various Countries,.. 99 4. The Manufacture of Peat-Briquettes,......101 Solid Peat-Slabs,.........101 Solid, Carbonized Peat-Briquettes,......103 Estimates of Cost of Operating Peat-Briquetting Plants,... 105 5. Manufacture of Mineral-Briquettes for Metallurgical Processes,.. 108 6. Manufacture of Artificial Stone-Masses,......112 7. Bibliography,...........115 Introduction. Briquetting is apparently a very simple operation, yet it has offered so many mechanical and chemical difficulties that it required almost a century to place it on a commercial basis. Since 1860, however, the progress has been steady and satisfactory, and to-day, for most of the European coal companies, the briquette-plant is a very profitable investment. Among the many applications of scientific knowledge to further economy by recovering and utilizing by-products and raw materials, there is possibly none which deserves the attention of Americans to a higher degree than briquetting. The recent miners' strike in Pennsylvania, which resulted in a scarce and irregular supply of coal at a high price, has advanced the possibilities for briquetting, and as a consequence public interest has grown rapidly. While the manufacture of coal-briquettes is not new in the United States, adverse conditions and sometimes lack of

Jan 1, 1905

By R. H. Wightman, G. H. Adams

H. C. WEED*—Referring to the use of "dummy fuse" for checking the shots in chute blasting operations, I believe that an even better practice is to blast the chutes with no delay electric blasting caps. Permanent wires can be strung through the grizzly lines and the lead wires from the shots attached to these lines. Using this method, no time is lost in spitting the individual fuses. The possibility of a fused charge becoming dislodged by previous shots and falling into the chute below is eliminated and there is no chance of a man walking back into his own blast. A small hand twist blasting machine or a radio "B" battery can be used to fire the shots if the lines are fired individually. If so desired the entire area can be blasted at once by a switch at the manway or in the drift below. providing a sufficient source of electricity is available. In case a switch is used, proper precaution for locking the switch must be provided. R. H. WIGHTMAN (author's reply) —We do use electric blasting when the number of shots is large; but we have found it more satisfactory to use fuse and caps for individual shots on the grizzly.

Jan 1, 1950

THE annual winter meeting of the A.I.M.E., which is to open in New York on Feb. 14, will be charac-terized by a number of novel features. The most important is that the technical sessions will be dis-tributed over four days instead of three as heretofore. This makes it possible to reduce the number of conflicts between sessions and also will enable each member to attend a larger number. At the same time the ses-sions are so arranged by groups that those interested only in one or more that are related can, if necessary, cover all in that group in three days as heretofore. The general excursion to which the fourth day has, for some years, been devoted has been regretfully given up, mainly because of the uncertainties of the weather in New York in February. In its place a series of group excursions are being offered at various times during the meeting, arranged, so far as possible, so as not to con-flict with any technical session likely to be of interest to those taking part in a particular excursion. Among the places to be shown the visitors are: the construction work on the Eighth Avenue subway, a real mining job; the Vehicular Tunnel, the world's greatest ventilating project; the manufacture of 42-in. conveying belts; one of the largest and most modern steam plants; a coal terminal; manufacture of mining equipment; a cable-making plant; an oil terminal and refinery. Other en-tertainment features include a smoker Monday evening with a real chance to get together and talk; an informal dance and entertainment given by the Woman's Auxiliary on Tuesday evening; the dinner-dance at the Waldorf Wednesday evening, with no long speeches; a general session Thursday evening when the Petroleum Division will present a series of important reviews of the year. An extensive program has been arranged for enter-taining the ladies, and members are urged to bring their wives. There will be dinners, teas, theater parties, shopping and sight-seeing excursions as well as the dances. The usual general luncheons for members, guests and ladies will be served each day at headquar-ters, and various committees and groups will hold lunch-eons, dinners, and round table conferences as indicated in the schedule on the page opposite. The Mining and Metallurgical Society of America and the American Society of Steel Treaters are participat-ing in this meeting and their members will be welcome as guests at any session or function. A joint conference of the Mining and Metallurgical Society and the A.I.M.E. has been arranged for Tuesday afternoon, under the chairmanship of Clinton H. Crane, at which the whole matter of the mineral reserves of this country is to be up for discussion.

Jan 2, 1927

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

By Donald Barton

THE theory of gravitation is based on Newton's law that any two bodies exert a mutual attraction which is proportional to the product of their masses and inversely proportional to the square of the distance between them; i. e. A= K MM/R2 (1) where K is a constant, M and m are the respective masses of the two bodies, and R the distance between them. In the earth's gravitational system, the earth is one of the bodies; the other may be any body within or without the earth. In theoretical discussions and calculations in regard to gravity, that other body usually is taken as a unit of mass: in the C. G. S. system, a body of one gram in mass.

Jan 1, 1928