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By Y. J. Wang

A critical path approach is presented for the problem of mine ventilation networks where regulators and fans are employed to control the airflow distribution. The problem is a classic one arising in mine ventilation planning. By identifying the analogy between the network for controlled flow and that for critical path method (CPM), the applications of the well known CPM technique to the ventilation problem become straightforward. The mathematical formulation of the problem is presented and the solutions are illustrated with examples. The cutset operation is introduced and employed for obtaining alternative solutions. The effects of booster fans on the total air power of the ventilation network are also discussed.

Jan 1, 1983

By L. V. Gregor, C. F. Aliotta, P. Balk

The structure of silicon surfaces, thermally oxi&zed in dry oxygen and in steam, was studied using the electron microscope. It was found that the structure on the original (etched) surface is retained at the outer surface of the oxide, whereas the oxide-silicon interface is smoothed out considerably. This supports the idea that, both in oxygen and in steam, the oxidation reaction occurs at the oxide-silicon interface. Mechanical damage of the original silicon surface affects the rate of oxidation. It also changes the chemical properties of the oxide, as shown by the enhanced rate of etching in buffered HF at the locations of damage. However, the oxide at the originally damaged surfaces still exhibits a high electrical breakdown strength. Exposure of thermal oxides to P205 or BzOs vapor, which will yieldphospho- or borosilicate layers, results in complete annihilation of all fine structure on the surface. Reaction of silicon with C02 gives a surface film which probably does not consist of pure SiO,. THERMAL oxidation of silicon yields uniform and strongly adhering oxide films which are normally amorphous and continuous. Contamination and surface imperfections have been reported to cause local crystallization and the formation of pinholes."' The parabolic-rate law of film growth observed by several workers for the oxidation both in steam and in dry oxygen at higher temperatures suggests that diffusion of one or more reactants through the oxide is the rate-deter mining step. One of the dif-fusants is an oxygen species and oxide is continuously formed at the oxide-silicon interface. This was concluded for high-pressure steam oxidation by Ligenza and spitzer5 from an infrared-absorption study of the isotopic exchange of oxygen. Jorgensen arrived at the same conclusion for the oxidation in dry oxygen by measuring during oxidation the resistance change between silicon and a porous platinum marker electrode in the oxide. Recently, Pliskin and Gnall' reported similar conclusions concerning the growth mechanism from controlled etch studies using a phosphosilicate marker. The work communicated in the present paper was aimed at studying oxide growth on locally damaged silicon substrates and relating it to the chemical behavior and electrical breakdown properties of the films. Since etched and oxidized silicon surfaces normally appear to be very smooth when examined by optical microscopy except for some occasional pits, it was decided to use the electron microscope as a tool. In this way, the detection of surface roughness and damage on a scale comparable to or smaller than the thickness of the film is possible. Also, the microstructure of the original substrate surface constitutes a built-in marker which represents a minimum of perturbation to the growing oxide layer, and no foreign material is introduced. Thus information on surface reactions and additional evidence on the location of oxide formation in steam and in oxygen could be obtained. EXPERIMENTAL Electron micrographs7 were obtained using a Philips EM100 electron microscope. Collodion surface replication was used since this is a nondestructive technique and thus permits replicating the same surface at different stages of processing. In order to establish the effect of different treatments it was found essential to make successive observations of the same area by using a reference point. Reference points were conveniently provided by scribing a small v mark on the original surface with a silicon carbide tip. This procedure yields damaged and damage-free areas near the reference point. Upon replication, the samples were thoroughly cleaned before subjecting them to the next process step. Mechanically lapped silicon wafers (Dow-Corning, 100 ohm-cm p-type, cut perpendicular to the (111) direction) were chemically polished in a rotating beaker with a mixture of 1 part HF (48 pct), 2 parts glacial acetic acid, and 3 parts HNO3 (70 pct) by volume. This procedure yields a smooth surface with a faint "orange peel'' structure due to a "ripple" less than 20002i deep. Oxidation in steam or oxygen was carried out in an Electroglas tube furnace. Steam oxidations were always preceded and followed by a brief exposure to oxygen at the same temperattre. The thicknesses of the oxide films under 3000A were determined with a Rudolph Model 436-2003 ellipsometer,' whereas those over 3000A were measured using the VAMFO technique. In the present study, a solution of 300 g of N&F in 25 ml HF (48 pct) and 450 ml water was used to detect areas of increased chemical reactivity in the

Jan 1, 1965

By P. W. Bridgman

FLOW and fracture are admittedly complicated phenomena of which we are yet only partially masters. There is not even universal agreement as to the details of the language best adapted merely to describe the phenomena, to say nothing of any theory. Certain points of view, however, are widely held, and there are certain general expectations as to what sort of procedures will prove permissible. A complete description of any situation involving fracture would demand a complete history of all the variables in the control of the experimenter. The experimenter endeavors so to choose his independent variables that they are adequate to determine completely the situation in the sense that when an experiment is repeated on the same initial material and with the independent variables running through the same sequence, all the other measurable properties of the system will also run through the same course. It is, I think, the universal conviction that when we are dealing with phenomena of flow and fracture, the most important of the necessary variables are the external forces acting on the various parts of the body; when the force history repeats, with certain obvious restrictions such as that temperature must be constant and non- mechanical forces, such as magnetic field, must be small enough to be ineffective, then the history of all measurable properties will repeat; in particular the alteration of geometrical shape due to flow will run through the same course, and when fracture comes, the character of the fracture will be reproduced. Complete mastery of merely the descriptive aspects of flow and fracture would demand the ability to predict the entire course of flow and complete characterization of the final fracture for every possible combination of forces, varying in time in all possible ways, when applied to bodies of all possible shapes. This full situation is obviously of prohibitive complexity. The first stage in reduction to manage- able simplicity is to resolve the total situation into the sum of contributions made by small elements. Our thesis is that if each of the elements is adequately characterized, the behavior of the whole system is fixed. The element is usually taken of a simple geometrical shape, suggested by the mathematics best adapted to the particular situation. The forces acting across the faces of the elements are ultimately determined by the forces acting across the free faces of the whole system. The detailed process of finding the precise forces on the faces of all the elements in terms of the external forces involves the use of a special mathematical invention, the stress, a constructional quantity consisting of six components. The stress at any point in the body is determined by both the external force system and by the physical properties of the body at all points; quite different stresses prevail at the interior of bodies of the same shape under the same external forces in the elastic and plastic ranges. The forces on the faces of any element are, however, uniquely determined by the stress system at the element. Our fundamental thesis

Jan 1, 1944

By C. D. Cochran, F. H. Deily, M. M. White, Victor Horner

A laboratory study of the effects of physical and easily measured rheological properties upon dynamic filtration was carried out. The purpose was to determine the factors affecting dynamic filtration and thus learn how to control this important property. The recommended procedure for determining the amount of fluid loss prescribed by API Code RP 29 "Field Procedure for Testing Drilling Fluids,"' is very useful for mud conditioning purposes, but inadequate for comparing filtration properties of different muds under dynamic conditions. Where dynamic filtration control becomes important for purposes such as logging and coring, other means of evaluating filtration properties are needed. A special device and testing technique were developed to provide reliable data on filtration characteristics of different fluids under dynamic conditions. Liquid saturated rock samples were drilled with a microbit, and the amount of connate liquid displaced by the fluid being investigated was measured. The empirical testing procedure was considered reliable. A large number of laboratory-prepared and field-mixed dritling fluids with a wide range of physical properties were studied. These properties included: (I) shape of consistency curves, (2) apparent viscosity, (3) plastic viscosity, (4) yield value, (5) density, and (6) API filter loss. Test results indicate that very little, if any, trend could be established between changes in these fluid properties and dynamic filtration. INTRODUCTION During the process of drilling, excessive loss of liquid from the mud to the formation is undesirable for many reasons. Filtration can reduce production-zone permeability, cause sloughing of formations, affect electric log curves, and render the fluid data obtained from cores unreliable. Thus, it is very important that we gain a knowledge of the factors that control filtration. It is generally agreed that in any type of filtration (static, dynamic, or combinations thereof), the mechanics of filtering depend in great part upon the composition of the fluid. Moreover, it is also true that the physical and rheological properties are influenced by the composition of the fluid. Indirectly, then, it was hypothesized that a relationship existed between dynamic filtration and physical-rheological properties, two effects of a common cause—fluid composition. This paper discusses an attempt to relate filtration-while-drilling to physical and easily measured rheological properties. It is believed that the results of this study may prove useful to others in the industry who are working on the problem of understanding filtration. The industry accepted practice for determining fluid loss from drilling mud is described in API Code RP 29. The practice is to measure the amount of filtrate that passes during a given interval of time from a quiescent drilling fluid under applied pressure through a piece of filter paper. This is primarily a test of static filtration properties. Other investigators have studied filtration under dynamic conditions. Williams5 and Pro-kop5 studied radial filtration and filter-cake buildup by circulating fluid through a porous cylinder under conditions similar to actual mud flow. Nowak,4 Krueger,3,4 and Vogel3 studied the effect of filtration upon permeability by flowing mud past the face of rock Samples. In their tests, the bit action was simulated by mechanical scrapers that kept the filter cake from building up. Ferguson and Klotz2 studied three types of filtration: static, dynamic, and beneath-the-bit. They investigated each type separately, using a model well in which bottom-hole hydraulics and mechanics were closely approximated.

Jan 1, 1958

By P. D. Gorsuch, D. L. Newhouse, Irvin R. Kramer

ALTHOUGH many methods have been suggested for the calculation of tensile strength and yield point from chemical composition, their usefulness has been limited to a particular cooling rate or section size. Further limitations have been imposed by failure to take into account many of the alloying elements that exert a considerable influence on the tensile strength or yield point. These systems, nevertheless, have filled an important need in many instances. The value of a system for the calculation of the tensile properties from the chemical composition and cooling rate is that it permits the prediction of the effect of alloying elements and heat-treatment on the mechanical, properties, so that more efficient use of alloying elements may be made. Furthermore, it aids in the choice of steel for a given application and tends to decrease the number of steels that otherwise would have to be tested. It is the purpose of this work to present a method of calculating tensile strength and yield point from the chemical composition and to suggest a method of correlating the tensile-strength and yield-point factors and cooling rate. Steelmakers have been interested for many years in the calculation of the tensile strength of hot-rolled steels. Quest and Washburn' summarize several of the attempts that have been made to devise formulas. They show the inadequacy of each of these formulas and present one of their own. It is apparent from their work that a simple additive equation of the type TS = A + BX + Cy + DZ + ? ? ? , where A, B, C, D, etc. are experimentally determined constants and x, y, z, etc., are the percentages of alloying elements present in the steel, is not adequate to analyze fully the situation encountered in the calculation of tensile strength. For example, it was found that the difference between the calculated and observed values became progressively greater as the carbon and manganese contents were increased. Therefore, the effect of manganese was given as a function of the carbon content. Grossmann,2 in his work on the hardenability of quenched steels, and Walters,3 in his method of calculation of tensile strength of normalized steels, present two cases in which multiplying factors were successfully used to express the combined effect of alloying elements. The factors in both cases were obtained from the fractional increase in hardenability or tensile strength with increase of alloy content. Yield point often is more important in design than tensile strength. For quenched and tempered steels a linear correlation exists between yield and tensile strength .4 This is not true, however, for normalized

Jan 1, 1946

By M. King Hubbert

DuRing the past summer the writer was asked by the Illinois State Geological Survey to make a study of some of its economic geological problems with regard to the applicability of geophysical methods of prospecting to their solution. The following four problems were suggested for investigation: (1) the fluorspar area of Southern Illinois, (2) oil structures in the south central part of the state, (3) the lead and zinc-bearing area of northwestern Illinois, and (4) the water supply and gravel deposits of the glacial drift. The prime requirements were to find a means of obtaining a maximum of useful information with a fairly modest outlay of expenditure for technical staff and equipment. The method of procedure adopted was that of making a preliminary study of each of the problems named by means of available office data and published reports with supplementary field reconnaissance where necessary. Preliminary Studies Fluorspar.—The fluorspar deposits of southern Illinois as shown by Weller,1 Bastin2 and others are of two main types: (1) vein deposits along steeply dipping normal fault planes, and (2) "blanket" deposits occurring practically horizontally along a certain sedimentary horizon. The vein deposits are composed mostly of calcite and fluorspar in sheetlike veins of thicknesses, where mined, ranging from about 2 to 12 ft. The surrounding topography is in a mature state of development with a relief of about 100 ft. or more. Any geophysical prospecting for this ore would have to depend either upon the physical properties of the ore and associated minerals or upon the properties of the geologic structure containing them. Fluorspar has a density of 3.18, which is somewhat greater than 2.7, that of calcite. Its

Jan 1, 1934

By D. A. Rice, R. L. Stone

Studies of the possible effect of plant water chemistry on the strength of unfired iron ore pellets apparently have not been reported in the literature. Naturally occurring soluble salts were removed from magnetic concentrate filter cakes obtained from several iron ore concentrators. Laboratory balling tests showed that unfired pellets made from these "clean" filter cakes were 50-100% stronger than the usual unfired pellets containing the salts. The fact that certain chemical additives dissolved in the water used for balling "clean" concentrates decreased the strength of unfired pellets indicates that salts in the plant process water may be responsible for lower strengths. According to chemical analyses of plant process waters at these plants, calcium and magnesium are probably the most detrimental salts in the plant circuits. It is suggested that calcium, magnesium, and other polyvalent cations in the mill process waters ion-exchange for lower-valence cations in the bentonite and thereby destroy the electrostatic-charge bonding in the green pellet. Some practical guidelines are also included for plant balling practices.

Jan 1, 1973

By Robert B. Fulton

Commercially, celestite (SrSO4) is the predominant strontium mineral. Among other strontium-bearing minerals, only strontianite (SrCO3) occurs commonly; however, it is rarely an item of commerce. Production of celestite is principally in Mexico, Spain, and Turkey. An attempt to produce celestite in Canada was unsuccessful. The United States, which is wholly dependent on imports, chiefly from Mexico (99%), is the largest consumer of strontium. Lesser quantities are consumed in Japan and Europe. The Federal Republic of Germany is the principal source of strontium compounds imported to the US. Uses The principal uses of strontium are for the manufacture of strontium carbonate and nitrate. Carbonate is used in glass for TV tube face plates and in ceramic ferrites for magnets. Nitrate is used in pyrotechnics, mainly in safety flares, to which it imparts a characteristic brilliant red color. Minor amounts of strontium compounds are used in electrolytic zinc manufacturing where the carbonate is used to remove unwanted lead. Small quantities are consumed in greases, ceramics, soaps, alloys, and pharmaceuticals. Specifications Typical celestite specifications for the carbonate and nitrate markets are shown in Table 1. Specifications of manufactured carbonate, sold in two grades, one to the glass industry and the other for ceramic ferrites, are shown in Table 2. Both grades of carbonate are shipped in palletized 50-lb bags. Glass grade material is shipped in bulk by rail. [ ] Manufacturing Processes The following description is adapted from Anon. (1980) . The manufacturing process for strontium carbonate and strontium nitrate chemicals is conceptually simple. Strontium nitrate is made from strontium carbonate in two additional steps. The production process begins with celestite, the natural form of strontium sulfate. In the first step the ore is crushed, ground, and mixed with coke. This mixture is then fed into a kiln where the ore is reduced at high temperatures to strontium sulfide; the coke is added to the ore as a source of energy and carbon. The carbon combines with the oxygen [ ]

Jan 1, 1983

By S. K. Kawatra, R. A. Seitz

The use of inferential particle sizing for closed wet grinding circuit control has been practiced for several years. This paper presents a review of some inferential sizing equations developed for pilot and industrial plants using regression analysis. An analytical development is then presented showing how the general inferential sizing model arises from the nature of the classifier model. The relation between the general sizing model and the individual equations is then discussed.

Jan 1, 1984

By A. D. Hughes

A relatively small area in Malaya, about 200 miles long by 40 miles wide, is the most important source of tin in the world. Some tin is recovered in other parts of the peninsula. Of the tin mined, 98 pct is recovered from alluvial deposits. From 1935 to 1941 the average annual world production of tin was 190,000 tons. The average annual production from Malaya during the same period was 62,000 tons or about one third of the total. Other producing countries, in order of importance, were the Netherlands East Indies 34,000 tons, Bolivia 30,000, Belgian Congo, Nigeria, Siam, Burma, China, and a few others with smaller amounts. The serious shortage of tin during the war period was due to the fact that the Japanese were occupying Malaya, Netherlands East Indies, Siam, Burma, and China which, together, formerly were producing 65 pct of the world supply. Because of the importance of tin in the world economy, and because of the fact that little is generally known in this country regarding the methods of recovering the tin in Malaya, it is believed that a short description of the industry, as carried on there, may be of interest to many of the readers. In addition you may be interested in the effect of the Japanese occupation, subsequent recovery of the properties and conditions existing at that time. The Malay Peninsula lies at the southeast tip of Asia. Singapore, a British colony, is situated on a small island at the southern end of the peninsula. It is a city of nearly a million population, an important world port, the site of a large British naval base and of one of the tin smelters. The Federation of Malaya consists of nine states, plus Penang, Malacca, and other small areas formerly part of the Straits Settlements, and it now covers the entire peninsula. The civil administration is controlled by the British. A constitution was adopted recently after reaching agreement with the Malay Sultans of the various states, who retain control of religious matters. The Capital is at Kuala Lumpur, a city of about 200,000 population, 250 miles north of Singapore and about half way to Penang. The country covers an area of 51,000 square miles, an area about equal to that of Florida and about one third that of California. It has a population of about seven million consisting of Malays, Chinese, East Indians, and a relatively small number of Europeans. The principal products are tin and rubber. There are over three million acres of planted rubber. The country is not self-supporting agriculturally as about one third of the necessary food supplies is imported. Rice is the principal food of the Asiatic population and some of the recent unrest is caused by a shortage of rice and the consequent high price. Good highways have been built through the settled part of the country. A railway, Government owned, extends from Singapore northward through the entire peninsula. The climate is tropical but health conditions are good for a tropical country. I was in Malaya from 1939 until January 1942, during the time of the simultaneous air attacks on Pearl Harbor, Manila, Hongkong, and Singa-

Jan 1, 1950

By E. J. Hall

(Butte Meeting, August, 1913.) THE iron-nail method of assaying has been used for a number of years, but has not met with the approval of all assayers. The method possesses advantages which may be given as follows : (1) no preliminary treatment is required ; (2) a lead button of proper size can be obtained (3) it is economical. On, the other hand, it has its disadvantages, which may be summed up as follows: (1) it is not applicable to ores containing large amounts of impurities other than sulphur, as practically all the base metals will contaminate the lead button ; (2) the slag is unsatisfactory in the larger number of fusions; (3) the method was known to give low silver results under certain conditions and the gold results were questionable. It was with the idea of determining the extent of this latter disadvantage that the following investigation was undertaken. It is well known that the fusion obtained in the lend assay is far more satisfactory than that in the " nails method " for gold and silver. The principal difference in the charges as a class is the presence of considerable reducing agent in the lead charge, and a limited oxidizing action in the nails charge, due to PbO. The possibility of improving the nails fusion by simulating the lead charge was the reason for using argol in some tests, even though there were reasons for expecting this would have -au objectionable effect on the results.

Jan 6, 1913

By Tadao Nagai, Masao Sato

Electrochemical measurements have been carried out in an auto- clave to investigate the electrochemistry of hydrogen precipitation of nickel from acetate buffered solution. After having previously obtained the rate equation for this reaction we have now made a concentrated effort to explain the rate equation electrochemically. A saturated NaC1-type Ag/AgC1 reference electrode has been improved so that it can be used in an autoclave. Polarization curves for the reaction, [H2=2H+ + 2e,] on nickel electrode were measured in solutions free from nickel ions at 185°C, and the parallel curves were obtained by changing PH2 and pH for normal and reverse reactions, respectively. Polarization curves in nickel solutions were complex, probably because the potential of hydrogen electrode is close to that of nickel and of the nickel surface altered during polarization. Then the nickel electrode potential and the reaction rate were measured simultaneously during pressure reduction at various hydrogen pressures and at various nickel concentrations. The reaction rates in terms of current density were plotted to obtain the local polarization curves for reactions Ni2+ + 2e ? Ni and H2 ?2H+ + 2e. The anodic and cathodic local polarization curves exhibit potential dependency. Therefore it is likely that the pres- sure reduction can be regarded as a coupled electrodes reaction.

Jan 1, 1973

By Raymond E. Zimmerman

Abstract-The Swirl Cyclone developed in Japan, although based upon the same principles as the standard cyclones for heavy-media or water-only cyclones for cleaning coal, is novel in that it is invested with the apex on top, discharging rejects at the top, and clean coal at the bottom. It also uses a variable air vent tube for controlling the vortex. Tests conducted indicate that its efficiency is not only as sharp as standard cyclones but it also performs using a much coarser grain magnetite, promising higher magnetite recovery. The author describes the results of tests conducted in Japan on a very difficult coal.

Jan 2, 1978

By J. R. Dawson, J. A. Glunt

Vesta No. 4 and 5 mines supply most of the high volatile coal required for Jones & Laughlin's by-product coke plants. Until 1944 all coal produced in these mines was loaded by hand. Pressure to mechanize at Vesta was brought on by the manpower shortage in World War II, and in 1943 a decision was made to change to mechanical loading. It was the opinion of those concerned that by use of selective mining the coal would be clean enough to be processed by the existing preparation plants. At that time coal cleaning at Jones & Laughlin consisted of hand picking the larger sizes at the mine tipples and wet washing at plants located at the Pittsburgh and Aliquippa Works. A typical section of the Pittsburgh seam as it occurs at Vesta is shown in Fig. 1. The 14 to 16 in. of drawslate immediately over the coal is too soft to be used for roof and must be taken down, leaving the rooster coal just above for roof. In selective mining an attempt is made to mine the coal under the drawslate first and then load out the drawslate separately as refuse. In full seam mining slate and coal are shot down at the same time and loaded out.

Dec 1, 1956

By Grover J. Holt

Open-pit mining on the iron range has been in a stage of transition for several years from the standpoint of mechanization. The most radical change in open-pit mining methods was started in open-pit haulage in 1937 with the departure from the then standard system of locomotive and car transportation and the advent of the heavy duty truck as a replacement. The initial use of trucks was followed shortly by the first installation of a conveyor belt for open-pit ore haulage. The growth of the combination of trucks for gathering units delivering to a conveyor system for transportation out of the pit, has been rapid and this transition appears to have reached a peak in 1949 with locomotives and cars now being used in only a few of the largest open pits. One point which must be considered, if we assume that the maximum equipment change- over point has been reached, is that the largest pits have probably passed their peak of production. Future ore replacement must come from smaller pits wherein the truck conveyor system has done an outstanding job.

Jan 1, 1950

By Merle L. Bowser, Lawrence W. Scott, John N. Murphy

The environmental status of underground mining operations is critical to the health and safety of the miners; particularly in a large mine, the multitude of interacting parameters that can favorably or adversely affect the environmental status makes the manpower requirement of the routine checking of specific areas and conditions a formidable one. While the concept of environmental monitoring for miners has been considered for some time, until recently the availability of sensors to reliably measure the parameters of interest severely limited the utility of such systems. The status of sensors for mine use and the evaluation of enviornmental monitoring systems is reviewed.

Jan 1, 1980

The early gazetteers mentioned the mining of coal in this state but gave no output data Several of the bulletins of the Illinois Coal Mine Investigations give the results of some historical studies of parts of the state and some early production figures, but some make no mention of this phase of the industry Reports to the state by the various railroads of tonnages carried give figures for coal carried, but usually do not specify its origin These figures, however, when used for roads which crossed the various coal producing counties, and divided between counties in accordance with the little data available have furnished the base for the most of the estimates of county productions Some county histories furnished a few facts, and some were obtained from various other sources

Jan 1, 1942

By Christopher Haycocks, J. Richard Lucas

The growth of computer and ground control technology in recent years, combined with an urgent demand for low-cost fossil fuels and mineral resources, has set the stage for full-scale utilization of computers in mine planning. Steeply rising production costs and the need to preserve the environment are placing great demands on engineers to improve their mining efficiencies, which can best be accomplished by applying the full capabilities of the computer. Pressure to develop and perfect programs with an immediate potential for improving mine design, reducing mining costs and extending the viable coal reserves of the country has already come to bear in the form of exploding energy requirements, environmental considerations and the visible limitations of other energy sources.

Jan 4, 1973

By Conrad W. Stellar, John L. Paynich

Design/Build concept that provides for earliest possible completion and lowest cost is presented. Elements of the program include: joint cooperation between owner, designer and builder; schedule construction sequence; and a line budget. Benefits over lump sum contracts are reviewed.

Jan 1, 1979

By L. W. Fagg

The purpose of this paper is to present in a convenient form data and examples necessary in making dynamometer card analyses; also to outline a procedure of well weighing. Many articles and papers have been written delving into the mathematical considerations relative to the shape and characteristics of dynamometer cards. However. it is recognized that there are too many unknown factors involved in such calculations to assure a workable degree of accuracy. For this reason the accepted procedure is to take dynamometer cards on wells in question rather than try to calculate the load curve. The polished rod dynamometer is now recognized as a necessary tool for measuring loads, torque, and horsepower. It is also used to determine pump action and trouble-shoot for any seemingly abnormal pumping condition. The apparently infinite variety of a = maximum load (height x scale constant) b = minimum load. Range of load is difference between maximum and minimum load speed—taken with stop watch stroke —measured at polished rod c = beginning of down stroke in direction of arrow. (End of up stroke) d = beginning of up stroke. (End of down stroke). Polished Rod Horsepower = (Area of card) x Scale const. x Stroke x Length x spm (Length of card) 33000x 12 1.35 1.35------x5300x 24 x 12 2.53 --------------------------= 2.06 23000x12 Appraximate Peak Torque: Upstroke = (2390) (12) (1) = 28,700 in. Ib Downstroke = (1 860) (12) (.866) = 19,300 in. Ib Counterbalance should be increased to make up stroke and down stroke peak torque equal. FIG. 1 dynamometer cards that can be obtained is one reason for the general lack of usage of the dynamometer as a control instrument rather than a means for making routine measurements of leads and horsepower. When it is considered that the dynamometer card is a record of the resultant of all forces acting on the polished rod at any particular instant during the pumping stroke. the problem is then one of breaking down this resultant into its various components. As a means of a quick review we shall consider the examples shown in Figs. 1 to 9: and Tables I and II and then proceed to the interpretation of variously shaped cards caused by some abnormal operating condition. In Table 11, when we were considering the factors involved in calculating the peak polished rod load, it can be seen that the factors involved greatly oversimplify the problem. Certain assumptions are made which may or may not he even close to the actual field conditions, such as the specific gravity of the fluid generally considered as one; that the crank has constant angular velocity; that the down-hole friction is zero; and that the fluid lift is from the pump. In the following examples we shall see what a variation in fluid weight and friction can do to the general shape and magnitude of the dynamometer card. (Figs. 10 to 22.) MAKING THE WELL STUDY It is obvious that it would be impractical to consider in detail all of these factors each time a well study is made, inasmuch as each well study job could conceivably be extended into a research project rather than serve the practical requirements of finding the answer to a specific problem. For this reason it is important that some objective be established previous to the time the well study is made. Load at TU = 3070 Ib Crank angle when polished rod is at position TU = ? ? = 30° Maximum counterbalance effect at polished rod = 2760 Ib Torque at TU = (Load at TU — Max. counterbalance effect-lbs) sin 0 x Length of Stroke 2 = (3070-2760) .5 x 24 = 1860 in. 15 2 Torque at TD = (Load at TD — Max. counterbalance effect-lbs) sin ? x Length of Stroke 2 = (530 - 2760) sin 330' x 24 = 13,400 in. Ib 2 Note: sin 0 from c to d on UPSTROKE will be positive value. sin 0 from c to d on DOWNSTROKE will be negative value Torque at c and d is zero because 0 is zero. FIG. 2 —APPROXIMATE METHOD FOR CALCUlATlNG TORQUE

Jan 1, 1950