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By AIME AIME

EVERYONE enjoyed the coal meeting and found it profitable. At least your correspondent did, and those to whom he talked. Close to a hundred were there. The Coronado proved an excellent headquarters hotel, though it is two miles or more from the business district of St. Louis; its Crystal Room was suitable for the technical sessions; its Lounge adequate for registration and informal chats; its Club Caprice made an artistic setting for the informal banquet; and its Coal Hole in the basement presumably served other needs-unfortunately we passed up an invitation to find out, and never got another. To be sure, the first day of the meeting (Monday, Oct. 28) was a drizzly one, but that only served to keep people inside where they belonged. Believe it or not, the first technical session was only five minutes late in getting tinder way, with H. N. Eavenson's words of welcome. M. M. Leighton then took over the conduct of the meeting, and invited Eugene McAuliffe to read his paper on how much coal the railroads are likely to use in the future. E. G. Bailey then presented some written discussion; among other things he wondered about the success of stokers on locomotives, and whether or not the burning of coal in locomotives could not he made a cleaner operation. Mr. McAuliffe pointed out that railroads are built to haul coal rather than to burn it. Maximum firebox efficiency is often subordinated to the traffic situation. Powdered-coal firing has not been a success because of limited firebox space. Stokers have resulted in economies indirectly, because large locomotives cannot he hand-fired and stokers thus make them possible. Nowadays it is not so important to do away with smoke, cinders, and soot, because most trains are sealed up and air-conditioned.

Jan 1, 1935

By Christopher Haycocks, Lawrence P. Johnson, George M. Neall, James M. Townsend

No method of roof control yet devised has proven to be universally acceptable for the wide range of strata conditions experienced in U. S. coal mines. However, a relatively new innovation, the roof truss, has proven itself capable of preventing roof failures which both conventional and resin bolting could not. Presently, the economics of roof trusses are not favorable when compared to bolting due primarily to drilling and installation procedures, but this is expected to change with improved truss and equipment designs. To realize the full potential of this new method of roof control, design criteria are needed which can optimize the effect of the truss for varying strata conditions. A review of the literature reveals that some work has been conducted on the roof truss. Cambrell and Haynes1 (1970) showed that the roof truss is superior to angled roofbolts installed through a header. Sheorey, Verma, and Singh2 (1973) used statics to prove that the optimum angle of inclination should be greater than 45°. However, to date, no systematic attempt has been made to establish design criteria. In this paper, the problem was approached in three ways. First, model studies were performed to determine general trends of truss support as a function of a number of variables. This provided a better understanding of the support mechanism involved. Secondly, beam theory was employed to calculate the actual support capacity of a truss, realizing the many simplifications, assumptions, and shortcomings of this approach to such a complicated problem. Last, field testing will be utilized to test the hypotheses previously developed and provide hard data to further synthesize roof truss design criteria. Field testing has recently commenced and should be complete before mid 1977.

Jan 1, 1979

By Linn M. Farish

SOVIET RUSSIA reserves must be stupendous. In 1937 I. M. Goubkin placed the reserves of all categories it approximately 48 billion barren which was about twenty billion horn Is in excel:, of all the oil produced in the world since 1857. It is not unlikely in fact it is probable, that these huge stores of petroleum may ultimately be proven to exist within the present boundaries of the U.S.S.R. The size of the country is almost beyond imagination it is 2.7 times as big as the United States. Great sedimentary basins exist in all its different geological provinces, much of which are entirely untested and barely prospected. Oil in commercial quantities is actually produced from formations in every period from the Devonian to the Pleistocene. In the Emba region alone, 300 salt domes are known with an estimate of 700 still to be found. Only 22 of the 300 have been drilled and all showed oil. Of the 22 domes drilled six are now producing. There are 400 mapped structures reported in Azerbaijan

Jan 1, 1940

By H. A. MEGRAW

THE meeting of the A. I. M. E. at Wilkes-Barre, Pa., Sept. 12 to 15, inclusive, celebrated the fiftieth anniversary of the Institute. It was at Wilkes-Barre, in 1871, that the foundation was laid for the great institution that now includes in its roster the greatest names. in mining engineering in every civilized country of the world. The founders of the Institute, with rare prescience, established a common ground upon which all mining engineers, whatever particular branch they might consider most pertinent, could stand securely, assured of a deep-seated interest from their brethren similarly minded in other localities. So wise and clear was the vision of the founders that every engineer connected with mining has found it beneficial, not to say indispensable, to maintain his connection with the Institute and to increase his technical enthusiasm through the medium of the valuable technical publications. The little coterie of 1871 has grown to a strong body of more than 10,000 members in 1921, reflecting the glory of the founders in the record of the accomplishments written on the pages of the fifty years of the

Jan 1, 1921

THE 125th meeting of the Institute was held in New York, Feb. 20-23, 1922, inclusive, and was the most successful annual meeting of the Institute ever held; there was a larger registration, there were more sessions of importance, and a greater number of sessions, than in any previous year. The total registration was 1331, comprising 351 New York members, 393 visiting members and 587 guests. At the annual business meeting of the Institute, held on Tuesday, Feb. 21, with President Ludlow presiding, there was a much larger attendance than usual. The report of the tellers was read and the following officers were declared elected: Arthur S. Dwight, Director and President-District 0 J. V. W. Reynders, Director and Vice-president-District 0 A. R. Ledoux, Director and Vice-president-District 0 Charles F. Rand. Director-District 0 George D. Barron, Director-District 0 William H. Bassett, Director-District 1 Thomas B. Stearns, Director-District 8 William Kelly, Director-District 5

Jan 3, 1922

By A. Roberts

This paper reviews progress in equipment design and in the techniques applied to mine lighting in Great Britain. The incidence of the disease miner's nystagmus, which was a major source of concern only a few years ago, has now diminished, largely owing to improvements in standards of lighting in mines. The reorganisation of the coal mining industry, involving increasing mech-anisation, together with new safety legislation, has brought about the widespread use of mains electric lighting underground. An account is given of some of the results of research to determine the lighting conditions needed for compliance with the compulsory legal requirement of "sufficient and suitable" general lighting at specific localities in British mines. Some details are given of the techniques applied and the results of recent research in the problem of glare from miners' cap lamps. Of the various factors in the working environment of the miner, it is true to say that lighting is seldom given attention comparable with that devoted to other factors, such as dust, heat and humidity, or atmospheric gas content. No doubt one reason for this lies in the ability of the human eye to adapt itself to low brightness levels. Be that as it may, the fact is that at the turn of the 20th century the miner's working light improved little throughout the centuries during which mining technology has developed. Indeed, in coal mines which encounter a methane explosion hazard, flame safety lamps, with a luminous intensity less than one candle power, were virtually the sole means of lighting during almost the whole of the 19th century. The 20th century has witnessed a substantial improvement in lighting techniques underground in coal and metalliferous mining. In Great Britain the general pattern has been one of standards periodically raised by the implementation of Statutory Regulations imposed under successive hlines Acts, but it is fair to add that the more progressive mining companies usually anticipated the Statutory Regulations, which when they have been put into effect have served to turn into general practice what was already being done at the better mines. In earlier years, official requirements were limited to the specification of approved lamp designs, with stipulated minimum values of luminous intensity and light output, but more recently the necessity of satisfactory maintenance of standards during service has been recognized, and the current regulations not only require that a maintenance organisation should exist, but also specify a maximum permissible depreciation below initial approval standards.'

Jan 1, 1961

By Marius R. Campbell

Does mine-sampling show the commercial value of a coal, and if so, how should it be done? This question is often asked, but seldom answered. During the past summer, while engaged in securing coal for the Government coal-testing plant at St. Louis, I had an excellent opportunity to obtain information on this subject, and the results seem to furnish an answer to the questions propounded above. Sampling for the Geological Survey Coal-Testing Plant. In organizing the work of the testing-plant, it was decided that coal in car-load lots only would be accepted for testing, also that this coal should be loaded under the immediate supervision of a representative of the plant, so as to be certain that the car-load sample would be representative. As an additional check on the work, two mine-samples were to be collected from each mine visited, and these samples, as well as the sam¬ple from the car when it was received at the testing-plant, were to be carefully analyzed at the chemical laboratory, which was established in connection with the plant and operated under the direction of Prof. N. W. Lord, of the Ohio State University, Columbus, Ohio. Mine-Sanmhling:-Mine-samples were collected with great care by me and my assistants, Messrs. J. Shober Burrows, John W. Groves and Frank W. De Wolf. The dominant idea in the regulations which were adopted for mine-sampling was that it should be done in such a manner that the sample would have the same composition as the commercial output of the mine. .

Sep 1, 1905

By Ivan E. Goodner, Charles H. Fulton

THE subject of the constitution of copper-iron mattes has received considerable attention in recent years by Keller,1 Bolles,2 Hofman,3 and Gibb and Philp.4 Still more recently Friedrich, Röntgen, Wiedmann, Heyn and Bauer, and Leroux have published, in some instances, elaborate researches on the various systems of the sulphides, and the sulphides and their respective metals, which enter into the constitution of mattes, and have added very greatly to the knowledge of the subject. The work of Friedrich has been especially fruitful. But to date no effort has been made to correlate the data obtained in the latter researches and apply then to the study of the product called " matte," which is made in such large quantities by copper and lead-smelters. In this paper we propose to determine, by metallographic and chemical means, the constitution of copper-iron and copper-lead mattes in the light of the recent data above mentioned. We do not discuss copper-nickel mattes or speisses (artificial arsenides). The paper is divided into three sections I. A review and discussion of the various binary systems of the metallic, sulphides, and the binary systems of various metals and their respective sulphides entering into the constitution of mattes; also a discussion of the physical and chemical properties of these sulphides. II. A description of the results obtained from the chemical and metallographic examinations of the samples of copper-iron and copper-lead-iron matte obtained from various plants.

Nov 1, 1908

By A Guinier

RECIPITATION in alloys is undoubtedly one of the most essential phase transformations in metallurgy and, besides, it is a phenomenon of great interest to physicists. It seems then that it can be chosen as a topic for an Annual IMD Lecture. Of course, the subject is a very wide one and I shall discuss here only a very restricted part of it. I should like to show why it is now considered that there is, at the beginning of the process, a stage distinct from the real precipitation, which is the pre-precipitation. We shall be chiefly interested in the atomic structure of the metal in this preprecipi-tation stage. Numerous reviews on this subject have been published recently.', ' The latest was given by H. K. Hardyh t the last meeting of the Institute of Metals in London. One of the most complete articles has been written by the late Dr. Geisler." I should like, at the beginning of this lecture, to pay a tribute to the memory of our friend Arthur Geisler. Some of the ideas which will be developed here are different from those advocated by him. But everybody knows the considerable progress in experiment and in theory which we owe to him and, personally, I deeply feel how fruitful have been the long discussions which we have had during many years. Experimental Basis of the Precipitation Problems Let us recall the essential facts pertaining to the problem of the precipitation. The starting point and the final one are well known. The initial stage is the supersaturated solid solution before quenching. The dissolved atoms replace some of the atoms of the solvent at the points of a definite lattice. It is generally considered that the distribution of the atoms is completely random, and that the lattice distortions are relatively weak. These assumptions are only an approximation. It has now beenproven", that, in some cases, the dissolved atoms have a tendency to segregate to form very small nuclei. These fluctuations of composition are greater than the normal statistical fluctuations in a purely random alloy. We shall see the role played by these nuclei later. The final state is obtained by a very long annealing at such a temperature that an equilibrium is reached in a reasonable time. The alloy is then composed of a matrix which is a saturated solid solution, much poorer than the initial one. Imbedded

Jan 1, 1957

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By William R. Jones, Robert M. Hernon

This report on the Central mining district of New Mexico is the partial culmination of an intensive U.S. Geological Survey effort dating back some 30 years. Robert M. Hernon went to Silver City in 1948 to finish a detailed restudy of the district that had been started in the thirties by Samuel G. Lasky. He was joined by William R. Jones in 1951, and Jones took over as project chief when Hernon resigned to do consulting work in 1953; it was under Jones' guidance that most of the work was brought to completion or nearly so ( 17, 22-24, 26-30). Hernon returned to the Survey in 1958 to work in .the southern Appalachians. Early in 1965 Jones urged that Hernon be reassigned to the Silver City project to help complete the Professional Paper report on the ore deposits of the Santa Rita quadrangle as well as to take over preparation of the report on the Central district for the Graton-Sales volume. This reassignment was approved, and Hernon began work on the present report. By late June he had completed most of it in draft form, and on June 28 Jones and Hernon left Denver for a short trip to Silver City to fill in a few gaps and to reacquaint Hernon with activities in the district, which he had not visited for 12 years. Late in the afternoon of June 29, 1965, as Bob and Bill were 85 miles short of their destination, their jeep collided head-on with a truck that was attempting to pass another vehicle in a cloud of dust. They both died instantly. As the most recent surviving member of the Silver City project (1958-1962), I was given the honorable though rather sorrowful task of putting the Hernon-Jones report "in shape" for publication. Fortunately the manuscript was already in good shape, so that the task has consisted of little more than minor reorganization and editing, and of preparation of the illustrations, abstract, and bibliography. The sections on wall-rock alteration had been left for Jones to complete in the light of his recently intensified interest in alteration geochemistry (25), and it is in these sections only that. the report may fall short, for they have been filled in from a 1958 manuscript by Jones on the ore deposits of the Santa Rita quadrangle that he intended to revise considerably. The shortcomings, however, are largely in the interpretation, not in the field data. As a brief but accurate summary of what was known about the geology of the Central mining district in 1965, this report stands as a fitting testimonial to the scientific dedication of two exceptional men.

Jan 1, 1968

By T. T. Read

JAPAN'S iron and steel industry has always been closely connected with military strategy. Many years ago it became evident that the country's iron-ore resources were too small to support any extensive industry. As a result a belief in the imperative necessity of securing such resources has influenced Japan's political and economic policy in the Far East. Iron-ore developments in China are too well known to need repeating except to note that they have been rather unsatisfactory to both China and Japan. The ore deposit at Tayeh, in China, is not as large as was first believed and, though that and other sources of supply in China proper are now furnishing Japan a little more than a million tons of ore yearly, it cannot be counted upon as a large permanent source of supply. The deposit in Shantung proved so disappointing on further exploration that operations there have, so far as I know, long since ended. The operations at Pen-bsi-hu, in South Manchuria, which C. F. Wang de¬scribed in the A.I.M.E. TRANSACTIONS for 1918, Vol. 59, were reported to have yielded 84,000 tons of pig iron in 1928 and about 50,000 in 1935, so they seem to be going back.

Jan 1, 1937

By AIME AIME

PLANS are now well advanced for the joint meeting of the Institute and over a dozen other engineering societies in Chicago during the week beginning June 26: Engineers' Week at A Century of Progress. All engineers planning to visit the Fair will find it to their advantage to be present at this time so far as the Chicago attractions are concerned, and Eastern members will also have the advantage of special transportation arrangements on June 24 and 25. The tentative program is given at the bottom of the next page. Monday morning, June 26, will be reserved for registration of members and guests and the Woman's Auxiliary at the Stevens Hotel, where special rooms will be provided. A luncheon will also be served there, and in the afternoon, a technical session on nonmetallics. Instead of having the big family dinner that evening at the Stevens, as at first proposed, the local committee has planned to have it at the Fair Grounds, where special facilities have been arranged. A meeting of the Board of Directors and a few invited guests will precede the dinner. All members and guests are likely to be interested in visiting the Museum of Science and Industry, so that will be the sole event on the program for Tuesday morning, June 27. The big attraction there at present is the model coal mine, the first operative coal mine ever built for exhibit purposes. It is based on the Deutsches Museum mine at Munich, but goes far beyond that in realism, and takes the visitor on an extended tour underground. It shows him in half an hour more types of modern mining machinery and coal geology than he would be likely to see in a week's underground study in the coal fields. The Institute members will be the first group to go through this mine.

Jan 1, 1933

By C. A. LINDBERG

Several new methods have been developed on the Iron Range to remove the material adhering to truck bodies in freezing weather. A machine known as a Gradall, incorporating the features of digging both above and below the horizontal, digging angle of blade control, full revolving, travel almost anywhere, and operated by one man, has proven successful in trials at body cleaning. Several of these units are in use with great saving in box-cleaning costs and improvements in efficiency of the truck operation with full capacity boxes. In addition to their winter use, the same machines have been used for ditching and excavating in the summer with great saving. The latest method of combating this freezing problem is to carry the exhaust from the engine through the body, making use of the tremendous heat that is now being wasted. To do this, the present wood sandwich which is used between the bottom of the box and the wear plate is removed and replaced with angles or channels run lengthwise of the box and spaced to permit gases to flow between or through them and also provide a good sup- port for the wear plate. The channels or angles are cut a little short on each end to form a cross passage that permits the gases to flow through the area. In the front end, openings are made in the wear plate and connect to a manifold created by welding a plate across the whole front of the box, spaced from the original end by the original vertical reinforcing angles at that point. The body being described is for a Euclid truck which is the only truck that has been adapted to this body-heating idea to date. At the rear of the truck, the holes from the cross passage are made in the bottom plate of the body and lead into a triangular-shaped body cross member under the scoop end of the truck.

Jan 1, 1949

By EDWARAD A. SIVEDENBORMG

REPORTS have been made at different times on the progress of water encroachment in the Frontier sands in the Salt. Creek oil field, Natrona county, Wyoming. All previous reports have, -however, been largely based on the position of water in the sands as determined by various physical tests. Subsequent information has been secured through a preliminary investigation of the porosity, grain size and degree of saturation of the Frontier sands. Also, a closer differentiation has been made between the waters encountered incident to the production of oil by means of chemical analysis. In view of the more recent developments there has been a need of a water encroachment map of the first Wall Creek based on a field survey and additional information acquired since the water encroachment map of the sand of 1926, by J. S. Ross and E. W. Henderson, petroleum engineers of the U. S. Geological Survey. The present report is confined to a study of the first Wall Creek sand and was written in connection with the preparation of the map, showing water encroachment in this sand. The first Wall Creek sand was the discovery sand in the field, the first well having been drilled in 1908. Its thickness averages 120 ft. and, varies between 90 and 160 ft. The sand is in the Colorado group of the Upper Cretaceous series and is further considered as a part of the Frontier formation found in other parts of Wyoming.

Jan 1, 1930

By Wallace E. Pratt

TO SERVE their primary function of balancing supply with demand. crude-oil prices must not only return full cost plus a reasonable earning to the efficient producer but they must also offer an additional reward to stimulate exploration sufficiently to maintain adequate reserves. High prices increase the volume and efficiency of exploration; low prig e- -Idle exploration. Over the last decade average prices for crude oil have been much lower than for the proceeding ten years, and lower even than the average over the life of industry. Under these circumstances no one should be surprised to learn that over this same recent period of discovery of new oil fields has also lagged and fallen below its average level for the previous decade. Crude oil prices have been too ion to support the required activity in wildcatting.

Jan 1, 1941

Coal - Surface Mining Coal Preparation Coal Utilization Research and Development Health and Safety

Jan 3, 1976

By M. W. BERNEWITZ

IT is 27 years since I last visited Broken Hill, New South Wales, one of the world's greatest lead-silver-zinc districts. Then, the flota¬tion of ores was in its infancy. The Minerals Separation process had its birth as a practicability in the Central Mill, which is still operating and yielding high recoveries. The average Australian knows that Broken Hill is an important mining center in a "corner" of New South Wales, but he does not know what a factor it is in the lead, silver, and zinc production of the world. Nor does he realize that among the ramifications arising from metal production at Broken Hill are the great lead smelter at Port Pirie, South Australia, 254 miles southeast; the electrolytic zinc works at Risdon, and the limestone mine at Davenport, Tasmania; the acid works at Cockle Creek, New

Jan 1, 1935

By F. S. Young

Previous laboratory and field experimentation has demonstrated the effect of several variables on drilling rate.1-5 These results have been incorporated into optimization theories6-" for the purpose of reducing drilling cost. Minimum-cost drilling theories rely on a combination of historical data and empirical prediction techniques for selecting optimum bit weight and rotary speed. Past solutions have required extensive use of computing equipment because of both the complexity of the mathematical formulations and the large number of parameters involved. Field attempts to apply these computed results have frequently failed because of the uncertainty of input data requirements. Humble has developed an on-site computer system to control bit weight and rotary speed and thereby implement the concepts of minimum-cost drilling. This system can (1) perform short interval drilling rate tests for formation evaluation, (2) use the results of these tests as input information to solve minimum-cost drilling formulas, and (3) control bit weight and rotary speed in accordance with these computed solutions. The purpose of this paper is to describe the computer control system and present results of initial field testing. Theoretical Considerations Minimum-cost drilling (MCD) requires a quantitative evaluation of the variables involved. Several forms of a basic mathematical model have been sug-gested.'?,' "he relationships reported here form the basis for the solution programmed in this work. Four equations are used, expressing drilling rate, bit bearing wear, bit tooth wear, and cost. A solution for minimum-cost drilling assuming constant bit weight and rotary speed over the entire bit life has been programmed for use in computing MCD schedules. This solution is subject to certain limiting assumptions such as those discussed by Graham et a1.I2: 1. Drilling cost is the summation of bit cost, rotating cost, connection cost and hoisting cost. 2. Diamond bits are excluded. 3. Bit life is limited by either bearing failure or tooth wear, or by a combination of operational factors that make it cheaper to pull an incompletely consumed bit. 4. Circulating hydraulics are adequate and do not limit drilling rate. 5. Bit weight considerations exclude hole deviation. 6. Drilling rate is a function of only bit weight, rotary speed, and degree of tooth dullness; that is, the effects of pressure, lithology, fluid properties hydraulics and drill string dynamics are ignored. In equation form, the four MCD expressions are as follows:

Jan 1, 1970