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By W. A. Boyer

HOISTS for metal mines are seldom designed for H one particular depth. They are intended for an ultimate load and depth with a given speed but are first used to hoist from a shallower depth, gradually working to the ultimate as development progresses. Sometimes the mine is not worked on the upper levels because of the kind and grade of ore, the mining of which depends on market conditions. In this case the hoist may be used in the same working shift to lift ore, for example, from the 1200 and the 4400-ft level. This means that the safety factor of the rope should be considered not only when it hoists from the greatest depth, but also when it hoists from the upper levels. According to present safety factor standards, a hoisting rope can have ample safety margin when hoisting from the lower or lowest level and still be shy of sufficient safety margin when hoisting from the upper levels. This will be shown by curves presented in this paper.

Jan 10, 1954

By F. J. Hurst

The rapid expansion of the phosphate fertilizer industry in conjunction with the projected shortage and spiraling price increase of uranium has greatly renewed interest in wet- process phosphoric acid as a significant source of uranium. Two attractive solvent extraction processes for recovering uranium from the acid have recently been developed and tested through bench-scale at Oak Ridge National Laboratory. One of the processes has been successfully tested on a pilot-plant scale at phosphate plants; the second process, which offers several potential advantages, still needs additional testing. The merits of each process are discussed.

Jan 1, 1978

By Howbert Van Dyne

THE Presidio mine of The American Metal Co. is situated in the "Big Bend" region, some 45 miles over state highway south of Marfa, a station on the Southern Pacific R.R. It lies 20 miles by road north of the Mexican border, in semidesert surroundings typical of this general section of the United States and the adjoining part of Mexico. All supplies are hauled in by truck from Marfa under contract. The concentrates and precipitates produced by the mill are carried by the same trucks to Marfa, from whence they are shipped, respectively, to the El Paso and Selby plants.

Jan 1, 1930

By Robert I. Kingman

SUFFICIENT testing has been performed with the Dutch State Mines Cyclone for thickening and desliming flotation feed at the concentrator of the National Lead Co., Tahawus, N. Y., to prove its application for this work. It is the purpose of this article to present some of the test results, operational details and advantages of cyclone thickening and classification. The metallurgy of the mill operation was described by Frank R. Milliken, assistant manager of the titanium division.l The present flowsheet for the recovery of ilmenite consists in grinding the crushing plant product in four open-end rod mills in closed circuit with mechanically vibrating screens to approximately -20 mesh. The screen undersize is treated in Crockett magnetic separators which produce three products: magnetic concentrate, nonmagnetic tailing containing ilmenite and gangue, and a Crockett slime overflow. The non- magnetic tailing is classified into eight sizer spigots products and a classifier overflow. The spigot sand products are tabled separately to produce a rough ilmenite concentrate, a middling product and a tailing. The table middlings are returned to Crockett feed. The table concentrate is dewatered and dried and further concentrated on Wetherill magnetic separators to produce the finished ilmenite concentrate.

Jan 8, 1950

The Library of the above-named Societies is open from 9 A.M. to 10 P.M. on all week-days, except holidays, from September 1 to June 30, and from 9 A.M. to 6 P.M. during July and August. The Library contains about 55,000 volumes, including sets of technical periodicals and the publications of scientific and technical societies. Members of the Institute, with few exceptions, are forced to spend a portion of their time in localities isolated from sources of information. To these the Library can render valuable service through correspondence; letters requesting information will receive special attention. The Library is prepared to furnish references and copies of articles on mining and metallurgical subjects; to determine the existence of mining maps, and to furnish general information as to the geology and mineral resources of all countries. All communications should be made as definite as possible so that the information received may be what is desired and not include collateral matter which may not be of interest. The time spent in searching for such collateral matter will be saved, and the information will be sent more. promptly and in more usable shape. The members of the Institute can be of service to the Library by forwarding copies of mining reports, maps privately issued, and similar material, which will be classified, indexed, and made available to other members. Suggestions for additions to the Library, either by purchase or personal solicitation as gifts, will be welcomed. It is hoped that members while in the city will use the Library freely, and assurance is given that most careful service will be rendered to them.

Jan 12, 1914

Continued discussion of the paper of R. W. Raymond, presented at the Cleveland meeting, October, 1912, and printed in Bulletin. No. 70, October, 1912, pp. 1111 to 1122. See also discussion printed in Bulletin No. 74, February, 1913, pp. 319 to 329. R. B. BRINSMADE, Puebla, Puebla., Mexico (communication to the Secretary *) :-Though I heartily approve of several minor points emphasized by Dr. Raymond (such as the general desirability of local administration, rather than Federal, and the evils inseparable from the Federal Apex Law), I feel obliged to dissent from his four final propositions. As Dr. G. 0. Smith has already discussed these propositions from the standpoint of the experience of other countries, I shall base my criticism upon certain general economic principles, which will be grouped under the following five topics: 1. The dual theory of property. 2. The essential factors in fixing prices. 3. The relation of land ownership to the distribution of wealth. 4. The relation of land ownership to speculation and development. 5. The relation of land ownership to the political power. I shall give here only a brief outline of these topics, as they are fully treated in the standard treatises on political economy.1

Jan 5, 1913

H ORACE VAUGHN WINCHELL was born at Galesburg, Michigan, Nov. 1, 1865, and died at Los Angeles, California, on July 28th of this year, at the age of fifty-seven. Mr. Winchell was one of the conspicuous geologists of his time. It may fairly be said that he was a geologist born and reared. His father, N. H. Winchell, was professor of geology at the University of Minnesota; his uncle, Alexander Winchell, was professor of geology at the University of Michigan. Under both of them Horace studied, graduat-ing at the University of Michigan in 1889. Mr. Winchell at once began that active life in the field which he followed for 34 years and until his death. The first years of his professional life were largely spent in the study of the iron ranges of Min-nesota. In 1898, he re-moved to Butte and became geologist in charge of the geological depart-ment of the Anaconda Copper Mining Co. and allied companies. There he remained for eight years. This period covered the trying days of the mining controversies be-tween the Anaconda and associated companies and the Heinze interests, and it fell to Mr. Winchell to direct the geological studies and development in connec-tion with that litigation. Recognizing the importance of careful geological study in the practical operation of mines, he organized and developed the splendid geological department of the Anaconda Copper Mining Co. This was one of his greatest contributions to the mining industry. Probably no mining company has attached the impor-tance to geological study and continuity of geological mapping in connection with mining operations that the Anaconda company has. It has given broad authority to its geological department and the development of its mines is under the direction of its geologists. The broad vision of Mr. Winchell was responsible for the adoption of this policy, one which is being profitably employed by many other organizations.

Jan 9, 1923

By H. T. Van Ells

The following is a brief description of the cost accounts in effect at the mines of the Anaconda Copper Mining Co. The accompanying chart, Table I., shows the distribution of labor, materials, and redistributable accounts to the various operating and repair accounts. OperatiNG. Development. Owing to the fact that every mine has its peculiarities in formation and methods, the question of arriving at what charges should be included under the head of " Development" is one that has occasioned considerable thought and comment, and in the cost sheet of the Anaconda Copper Mining Co. this account has been sub-divided to show the expenses of breaking ground, tramming, timbering, shaft sinking, up-raising, and cutting stations and skip chutes. It has always been the policy of the company to charge the entire cost of this work to operations monthly, whether the mines are producing or not, also the cost of the opening up of new mines; and only surface construction and additions are charged to capital, excepting original machinery installed for operating pumping plants. Explanations of the charges to the various sub-accounts follow : Breaking Ground.—Work performed in driving cross-cuts from the station, or cross-cuts from the drifts, and diamond-drill work, for the purpose of discovering or developing ore bodies. Tramming.—Cost of tramming waste produced by cross-cuts mentioned above. When waste is hoisted to another level to be used for filling, the charge to this account stops at the station, and when hoisted to surface the charge includes tramming from the collar of the shaft to the dump. Timbering.—Cost of timbering the cross-cuts mentioned above includes the cost of handling and framing such timbers, but does not include the wages of station tenders and top carmen.

Jan 1, 1914

By George Smith

TWELVE years ago, the Director of the United States Geological Survey addressed to the Secretary of the Interior a letter calling attention to the government's need for liquid fuel for naval use and pointing out that the rate of increase in demand was more rapid than the increase in production.1 This letter, in a way, inaugurated the policy of public oil-land withdrawals, which was well founded in its primary purpose of protecting the oil industry and highly desirable in its immediate effect of checking the over-development of that day in California. Unfortunately, however, through delays in legislation, this policy may be regarded now as having outlived both its intent and its usefulness. In 1908, the country's production of oil was 178,500,000 bbl., and there was a surplus above consumption of more than 20,000,000 bbl. available to go into storage.: In 1918, 10 years later, the oil wells of the United States yielded 356,000,000 bbl.-nearly twice the yield of 1908-but to meet the demands of the increased consumption more than 24,000,000 bbl. had to be drawn from storage. Nor is this all of the brief comparison. In 1918, our excess of imports over exports of crude petroleum was nearly 33,000,000 bbl. whereas in 1908 we exported 3,500,000 bbl., which was net, as we had not begun to import Mexican oil. In this period, the annual fuel-oil consumption of the railroads alone has increased from 16,871,000 to 36,714,000. bbl.; the annual gasoline production from 540,000,000 gal. to 3,500,000,000 gal. This record may be taken not only as justifying the earlier appeal for Federal action, but as warranting deliberate attention to the oil problem of today.

Jan 1, 1920

By C. N. Schuette

THE producers of this liquid metal call it quicksilver, while the consumer generally refers to it as mercury. It is one of he seven metals that were known to the ancients. These seven were gold, silver, iron, copper, quicksilver, lead, and tin. Other metals were sometimes accidentally alloyed with some of these, but it was not until 1490 that antimony, for example, was discovered and identified as a separate metal. It is not surprising that quicksilver should have been known in ancient or even in prehistoric times, as globules of the native metal often occur in the outcrops of the ore. Furthermore, the first man to build a fire on an outcropping of quicksilver ore would probably have found globules of quicksilver in the cold ashes of his fire after it burned out. The inability to pick up the globules with the fingers would excite interest and an attempt to gather it in shells or gourds to be exhibited and traded. The ore of quicksilver is the red sulfide, cinnabar, which has been mined and used as the pigment vermilion since before the beginning of written history. In recorded history, quicksilver is first mentioned in documents by Aristotle, 384-322 B.C. Theophrastus, in 315 B.C., credited the Athenian, Callias, with the invention of methods to beneficiate cinnabar in 415 B.C. In China also there are records antedating Christ which mention both vermilion paint and the fluid metal. From these early records, it seems certain that not only was cinnabar used as a pigment in those days but also that the metal was reduced from the ore and was used for amalgamation, for gilding, and for medicinal purposes. Quicksilver mining and metal-

Jan 1, 1953

Since 1571, when the Institute was founded, many of the most important papers in the English language, on the various phases of mining and metallurgy, have appeared as Institute publications. As members of the Institute regularly receive the publications in which they are interested, this discussion is primarily for nonmembers who wish to know of them. The Institute has several means of issuing papers which have been submitted and accepted. The monthly journal, Mining and Metallurgy, is the magazine of the Institute. In it appear notices and reports of official business as well as many papers and contributions which do not appear otherwise. The annual subscription price of the magazine to nonmembers is $3 per year; Canadian and foreign postage $1 extra; single copies 50 cents; back issues $1 each. Many papers are published separately each year. They are issued in one or the other of two numbered series; namely, Technical Publications and Contributions, and of the latter there are four forms: Preprints, Mimeographs, Reprints, and Unpublished Manuscripts. A Technical Publication or Contribution (in any form) is issued by the Institute when it is listed in Mining and Metallurgy. Technical Publications are sent automatically to members who have asked in advance for papers on a given subject. All members are entitled to a copy of every paper in either series, except when a Contribution is an Unpublished Manuscript. Con¬tributions in the form of Unpublished Manuscripts are filed in the Engineering Societies Library and copies of some of these papers may be found in a few selected libraries throughout the country.

Jan 1, 1933

Homestake's Bulldog Mountain Operation near Creede, Colorado, in the San Juan Mountains at an elevation of nearly 2,750 m (9,000 ft), is subjected to short summers and long cold winters. Creede’s history dates back to 1889 when silver ore was discovered; and by 1892 production of over a million dollars per month was being shipped from mines located along the Amethyst Fault. The Bulldog Mountain Fault remained relatively untouched by the early prospectors. The United States Geological Survey recognized the potential of this fault in 1960, which led to the staking of many claims over the structure. Homestake leased properties in 1963 and in mid- 1964 a tunnel was started at the 2,956 m (9,700 ft) level with encouraging mineralization being encountered. In 1968 a decision was reached to build a flotation mill of 318 mtpd (350 stpd) capacity. The erection of the mill was completed in early 1969, six years after the first exploration was begun. Since initial start-up, extensive drifting has been done on several separate levels. Two underground hoist installations serve the various levels and many thousand feet of vertical mining operations. Due to the unconsolidated nature of the vein, a new unique underhand cut-and- fill mining method was developed. This procedure is the reverse of the normal cut-and-fill and proceeds from the top down under cemented sand fill, which, while expensive, has greatly reduced s toping hazards. Prior to 1977, a considerable quantity of silver was lost in the slime fraction of the ores processed because of oxidation and other inherent characteristics of individual minerals. Due to Homestakefs favorable experience in treating the slime fraction of the Lead, South Dakota gold ores, experiments with leach methods to recover silver from the slimes by Carbon -In -Pulp offered' the potential for additional silver recovery. Work was begun on the Carbon-In-Pulp plant in April 1976 and completed in December of that year at a cost slightly exceeding $2 million. The C. I. P. plant was designed for 136 mtpd (150 stpd) of current plant slimes plus 227 mtpd (250 stpd) of slimes dredged from the old tailings during the summer season. The sand fraction of the flotation

Jan 1, 1981

INTRODUCTION Great emphasis has been given throughout this text to the necessity of maintaining the integrity of mineralogical populations when operating upon sample data drawn from mixed populations. Mineral deposits rarely are completely homogeneous and often consist of many subsets separated by geological and mineralogical boundaries. Sometimes different mineral populations are difficult to distinguish, and may be inadvertently lumped together-often without serious consequences, but more often with detrimental effects upon analytical results. The geologist must accept the responsibility for recognizing and recording mineral boundaries that may include: changes in mineral suites, lithological horizons, host rock types, faulted and offset segments, zones of enrichment or depletion, and several other geological and mineralogical changes that effect mineralogical structuring and distribution within a deposit. When employing conventional methods for assigning estimated values to irregularly shaped mineral inventory blocks, it was only necessary for the geologist or engineer to con- fine the block limits to the known geologic boundaries. Thus if a fault interrupted the mineral zone, the trace of the fault could be used as a block boundary. Intelligent decisions could always be made as to which blocks to include in each mineral population. However, with the advent of the computer, which per- mits the computation of mineral inventory blocks using better mathematical estimation techniques, there now enters the "boundary problem." Unless the computer can be programmed to recognize population differences and geologic boundaries, greater estimation errors will be found in computer-generated mineral reserves rather than in less sophisticated conventional inventories. Much disillusionment has been expressed over the years by experienced mineral appraisers as a result of their study of computer-generated inventories that failed to account adequately for geologic vagaries. Many, thus disillusioned, have concluded that computer techniques are not satisfactory, or have only limited applications to simple deposits. As with all problems in the mineral industry,

Jan 1, 1980

WILLIAM H. KOBBÉ (communication to the Secretary*).-I have read with much interest the discussion of my paper by Arthur Knapp and I. N. Knapp published in the March Bulletin. These discussions apparently assume that my paper advances a. number of ideas that are not intended: 1. That the total sandbody or pay is to be removed. 2. That upon bringing this sand and oil to the surface 100 per cent., or perfect separation, can take place. 3. That this tremendous quantity of sand is then hauled away in wagons and distributed as road material. The paper raider discussion is not a theoretical treatment of the subject but is the result of actual experience in oil production under the conditions mentioned.. That wells that produce sand produce in ore oil, and the best operating methods to bring this about are fully treated. It is, of course, impossible to remove all the oil sand underlying a property, but the greater the amount removed the greater becomes the production of oil. As stated in my paper, the surface disposal of this large volume of sand is a problem and the only use to which it can be put is road surfacing; but I did not intend to convey the idea that all this sand was thus used. Only a very small quantity was required on the company's roads, and two wagons only were employed for this purpose. The remaining sand accumulated in the numerous "washes" and sumps. Although this sand contained sufficient oil to stain the hands, it was, surprisingly dry and could be easily shoveled. As stated in the paper, "the piles of sand are gradually freed of their oil content and a crust forms on their surface which will bear the weight of a man." I consider this a high degree of separation. A small amount of oil necessarily remains in the sand and is held there by capillarity. Otherwise it would be useless as a road binder, and, furthermore, to recover such oil special processes of treating are required. Arthur Knapp says, "of the total volume produced by pumping, not more than 4 or 5 per cent. can possibly be sand." I cannot agree with this statement as I have managed many properties where the wells were so operated that the amount of sand produced was five times this figure.

Jan 6, 1917

By J. E. Pogue, F. G. Coqueron

This paper describes the sources of funds required by the petroleum industry to finance capital expenditures and also presents a discussion of the effect of rising construction costs on these expenditures. The petroleum industry obtains its capital funds from several sources: (I) internal, from retained cash earnings; and (2) external, from borrowings and the sale of securities to the public. The upward trend of capital expenditures of the petroleum industry is caused in the main by the influence of two powerful factors: (I) the physical growth in the demand for oils; and (2) the rising cost of drilling wells and constructing refineries, pipe lines, and other facilities. The segregation of these factors is accomplished by deflating the actual capital expenditures so that they are shown in terms of 1939 costs and then subtracting the adjusted series from the actual figures to yield a set of data representing the expenditures made on account of higher costs. Rising costs affect prices and the portion attributable to this factor had to be generated from the cash earnings of the industry, which called for higher oil prices. Introduction Capital may be defined as "wealth employed in or available for production." All production requires capital. Expanding industries require more capital than static ones, and technological industries employ more capital than. those in which little equipment is needed. The petroleum industry is both rapidly growing and highly technological, and, being a large industry, its capital requirements are prodigious, amounting to about one-seventh of the total of all American business, excluding agriculture.* Capital formation may be defined as the method by which the wealth or capital needed in the productive processes is created. There are various ways in which capital funds may be obtained but there is only one way in which capital can be created—out of production in excess of consumption, that is, savings. The physical realities are simple, but the monetary concepts are complicated because the mechanism of credit can draw upon future savings. Source of Capital Funds An industry, such as the petroleum industry, can obtain its capital funds from

Jan 1, 1949

By H. Siebert, G. Raitt

With the advent of the Interstate Highway Pro- gram, many problems have been encountered in the application of highway design standards to topography, particularly rock cut design. A rigid application of slope ratios with little respect to rock type, dip, foliation, structure and height of cut face is a problem. Generally a slope ratio of ½ : 1 or 63º for shallow cuts and 1/3: 1 or 71º in deeper cuts are used in Connecticut. The deepest cut face constructed recently was greater than 185 ft. With cuts of this size, rock fall and stability become a problem, and a way to reduce the problem is to construct a stable face initially. A search of the literature indicates that adequate information on the construction of stable rock slopes is not available. A major highway contract was awarded in 1962 to Savin Brothers, Inc., in which line drilling on 6-in. centers was required in many portions of the contract where the cut was greater than 60 ft and one or more benches were to be constructed. From the start of the project many variations were attempted regarding slope hole spacing and distribution of explosives in the holes. Rock ranged from a competent granitic gneiss to an incompetent soft graphitic schist. Generally, the roadway alignment was roughly normal to the strike of the foliation having a dip of ± 60º. An important factor affecting construction of rock slopes was the existence of intersecting joints and faults. The spacing used in less competent rock was about one ft on center. Loading of holes was purposely varied. As competency of the rock increased, hole spacing was also increased. Thus, on a different project in similar rock, spacing was kept at 4 ft.

Jan 4, 1966

By W. J. Sharwood

The assay or estimation of the total gold content of an ore presents little difficulty, when circumstances permit of securing a thoroughly representative sample. The general practice has been fairly standardized, and such errors as occur in the results obtained are for the most part attributable to the methods of sampling rather than to those of assaying, while duplicate assays made by skilled workers usually agree closely. When it is a question of estimating the "free" or amalgamable gold of an ore, as opposed to the total gold, there is but little uniformity in the methods employed by different workers, and often equally little in the results obtained when duplicate determinations are attempted, no satisfactory standard method having been generally adopted. The methods in use are of two general types—"panning" and "amalgamation." Panning For the estimation of the value of the visible gold by panning or washing, a weighed sample may be taken, ranging from an ounce to several pounds; a kilogram or 2 lb. is a favorite quantity for laboratory tests, while a prospector often uses a full miners' pan, say nearly 20 lb. or 10 kg. In the case of rich quartz, ground to about 30 or 40 mesh, a Mexican horn is convenient, using 1 to 8 02;. of material, and a 6-in. frying pan is favored by many prospectors in dry districts. Bateas, plaques, and dishes of various patterns are used for the same purpose. With these, fairly close results may be obtained by using for ocular comparison standards consisting of weighed amounts of gold of similar character as regards purity, fineness of division, and the general shape of the particles, which standards are preferably obtained from gold of the same locality, or the same deposit, as the ore or gravel being tested. Men working in one particular district sometimes become surprisingly expert in thus judging the value of an ore by the eye, the weights of both ore and gold being guessed. On the other hand, many have been led to overestimate the value of ore and gravel from unfamiliar localities, where the gold has been very finely divided or of unusually high silver content, and a novice may

Jan 1, 1916

By E. E. Malouf

With the continued development of low-grade porphyry copper deposits by open pit mining, substantial amounts of copper-bearing strip material have been accumulated in waste dumps adjacent to the many large mines. Since the end of World War II, the production of copper from leaching these copper-bearing wastes increased from approximately 4% of the total copper production to 10% by the early 1960's. Projected increases will probably raise this figure to 20 to 30% by the early 1970's. Furthermore, a gradual recognition of the economic feasibility of leaching mined-out areas is evident and will undoubtedly contribute additional production. Waste dumps in canyons and gulches on the periphery of open pit mines, mine stopes, caved areas, and abandoned open pits often contain substantial quantities of leachable rock ranging in concentration from 0.1 to 0.4% copper. Recent developments in the leaching of copper, mainly the recognition of bacterial oxidation of sulfide minerals combined with better under- standing of the control of the salt content of the leach solutions, both by adjusting the pH and/or by hydrolysis, are resulting in a greatly expanded recovery of copper from these hitherto uneconomic mine rejects. 11.5-1. Mechanism of Leaching. Leaching processes for the extraction of metal values from mine ore or waste may be classified for convenience as either chemical leaching or bacterial leaching. Chemical leaching is considered to be the extraction of soluble salts by metathesis in acidic, basic, or neutral water solutions. The reactions involved may be evaluated by chemical thermodynamics. Bacterial leaching, although a chemical process, is dependent on biological catalysis and this is generally a much more complex process. This justifies its separate treatment in the application to leaching. Acid ferric sulfate solutions are commonly employed in the mining industry to leach valuable metals from metal sulfide ores. The leaching mechanism is a reduction-oxidation reaction in which minerals are oxidized at the expense of ferric sulfate. Such chemical leaching is profitable when

Jan 1, 1968

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

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Jan 1, 1907