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By THOMAS LEONBRD WATSON

I. INTRODUCTION. THE results embodied in this paper are based on a careful field- and laboratory-study of the lead- and zinc-deposits of the Virginia-Tennessee district, begun in the latter part of the summer of 1904 and completed in the spring of 1905, preparatory to the publishing of a State report .on them. A separate description of the individual deposits in Virginia is purposely omitted, since I have already described them in considerable detail in a State report. The Tennessee deposits are described here in some detail for the reason that no detailed record of them has yet been published. Practically, this paper summarizes the results obtained from a study of the geology of the ore-deposits of the district as, a whole. (I had the pleasure of visiting the deposits of Virginia and Tennessee with Dr. H. Foster Bain of the U. S. Geological Survey, in April, 1905. Figs. 21 and 22 are from photographs taken by Dr., Bail.) II. HISTORICAL. . The first authentic records of lead-mining .in Virginia date hack more than 150 years; and the old lead-mines at Austinville, on New river in Wythe county, V a., were the first to be worked. Colonel Chiswell, a native of Wales, and one of the earlier adventurers in southwestern Virginia, was one of the first operators of the Austinville mines. Chiswell's operations at Austinville commenced in the year 1750, and closed shortly after the beginning of the Revolutionary War, in the' year 1776, covering a period of about 25 years. From that time to the present, mining has been carried on almost continuously in the Virginia area. For many years after the Virginia mines were operated, mining was confined exclusively to the lead-ores. The zinc-ores

Mar 1, 1906

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By D. W. Smith, Robert F. Mehl

It has been shown by numerous studies that the orientations of new metal crystals are determined by the orientations of the crystals in the original matrix, whether these new crystals are formed by recrystalliza-tion, by precipitation from solid solutions, or by transitions in the solid state. The orientations of crystals formed by recrystallization of cold-worked metals that bear preferred orientations are occasionally simply related to the initial preferred orientation; often, however, the relationship is not simple, but complicated and obscure in origin.1 The orientations of crystals formed by precipitation from solid solutions have been shown by many studies in this and other countries to be determined by the orientation of the crystals of the solid solution stable at the higher temperatures, though here again complicated cases have been found and no general theory is available.2 Related to this latter class are the relationships found in crystals formed by suppressed transforma-

Jan 1, 1935

By J. E. Campbell, A. W. Wesner, M. Pobereskin

This paper summarizes the results of an investigation sponsored by The Coates Steel Products Company. The objective was to determine the relative effects of certain chemical and physical properties on the wear resistance of grinding balls when grinding cement. In making this study, a number of types of balls were used in both dry and wet grinding in commercial ball mills. The radioactive-tracer technique was used in separating the test balls from the rest of the mill charge and in sorting the different types of halls that were all tested at the same time for each of the grinding operations. PROCESSING OF GRINDING BALLS In order to determine whether the properties of grinding balls, namely, composition, microstructure and hardness, can be related to the rate of wear, the halls used in this study were selected to represent various combinations of these properties. It was recognized that the mechanism of wear was not the same in the wet mill as in the dry mill. Therefore, the types of balls tested in each of the two environments were not necessarily the same. However, all of the types of balls evaluated in the dry mill were tested simultaneously for one time period, while those evaluated in the wet mill were tested simultaneously for three different time periods. All of the test balls were separated from the charge when the mill was dumped. All of the balls were of 0.940-inch diameter when charged, and all but the regular production balls were finish ground to this size to eliminate the decarburized surface layers. The steels and processing methods used, as well as the micro-structures and hardness levels of the balls, are described as follows: Regular production forged SAE 1095 steel balls were used in both the wet and dry mills. They were forged to a nominal diameter of 0.940 inch and quenched in oil from the forging temperature. Each retained a partially decarburized surface layer from the forging bar stock; the maximum depth of this layer was about 0.030 inch and the decarburization was negligible where the ball was sheared from the bar. The hardness at the surface was 40 to 46 Rock-well C in the partially decarburized area and 57 to 62 Rockwell C in the areas not decarburized. The hardened zone extended to a depth of about one-third of the radius. Below the decarburized layer, the hardened zone consisted primarily of hard as-quenched martensite with varying amounts of retained austenite. This structure changed to fine pearlite at a depth of about one-third of the radius. In order to eliminate the effect of the decarburized layer, a set of production balls of SAE 1095 steel was forged to about a 1-inch diameter, quenched in oil from the forging temperature, and ground on ball-bearing grinding equipment to a 0.940-inch diameter to remove the decarburized layer. The balls' hardened zones were similar to those in the previous set. The hardness of the finished surfaces was 52 to 60 Rockwell C. A slight amount of decarburization apparently remained after the removal of about 0.030 inch from the surface. Balls of this type were tested in the dry mill only. Another set of forged SAE 1095 steel balls of 1-inch diameter was heated to 1500 F and quenched

Jan 1, 1961

By F. T. Davis

Many contributors have added to the fund of knowledge in the basic sciences related to mineral dressing during the past year. During 1964, the French edition of the Proceedings of the VIth International Mineral Processing Congress together with discussions was printed. Also, complete Preprints of papers delivered at the VIIth IMPC were published in September1. Over a third of the papers presented at VIIth IMPC dealt with fundamentals. COMMINUTION It has been postulated by Ponceleta that flaws need not exist before a stress is applied but rather the flaws are created at the tip of a propagating crack at a stress well below the theoretical breaking stress.

Jan 2, 1965

By H. M. Chance

Jan 1, 1886

By J. M. Boutwell

I. Introduction. THE object of this paper is to present a concise statement on the genesis of the copper- and lead-deposits of the Bingham Mining District, Utah. It is essentially a condensation of a chapter in a detailed report on this district, together with so much on geologic features, and on the character and occurrence of the ores as bears on the problems of ore-deposition. The studies upon which the paper is based were undertaken in 1900 under the direction of S. F. Emmons, Geologist-in-Charge of the Section of Metalliferous Deposits, U. S. Geological Survey; and a little additional data was secured in subsequent years. The evidence then obtained as to the genesis of the replacement copper-ores has led, to conclusions which differ somewhat from explanations hitherto current. Accordingly, it seems desirable briefly to present the facts together with the resulting conclusions in a separate paper.

Nov 1, 1905

By F. E. ROGERS

CUSHMAN TUNNEL No. 2 is adjacent to the Hood Canal, near potlatch, Wash. It is 17 ft. inside .diameter, about 13,000 ft., or two and one- half, miles in length, and is a part of the second unit of the Cushman power project. It connects Cushman ' Dam No. 2 and the penstocks that lead to the power house on the beach about 400 ft. vertically below the outlet of the tunnel. One shaft, 190 ft. deep, and two adits between 300 and 400 ft. long, were provided to speed up driving operations. his arrangement gave 6 working headings, which were operated 24 hr. daily. The shaft provided a manway, cageway, and skipway.

Jan 1, 1931

By Claude P. Heiner

While the title of this paper embraces the entire West Coast, the author, in the interest of simplification. has confined the discussion to California-particularly the central section. California's population has, risen 45 pct since 1940. Its electric requirements have also increased, not only because of the growth in industry and population but also because of the widespread tendency of all types of electric consumers to use more electricity than ever before. The growth of California's electric utilities is shown by published data covering operations, of three of its large systems and is given in Table 1.

Jan 1, 1949

By J. B. Dilworth

I. INTRODUCTION. THE purpose of this paper is, first, to give a general account of a little-known coal-district of SE. Kentucky, its topography, drainage, and mineral resources, for those who may be interested in its economic development; and secondly, so to describe the geologic features of the field as to furnish available data to those engaged on the broader problems of Appalachian coal-geology. The data from which the major portion of the paper has been prepared were obtained, in professional investigations for private individuals and corporations, within the last decade. The area under review, defined by a heavy line on the map, Fig. 1, lies between Little Black and Pine mountains, and extends from Harlan on the west to a N-S. line crossing Looney creek 3 miles from its mouth on the east. This area can be divided for description into a Western and an Eastern Division. The character of investigation pursued in the Western Division, below Fugitt creek, was very different from that employed in the Eastern. In the former, only a rapid reconnoissance was attempted : such coal-openings as had been made by prospectors or by citizens in obtaining fuel were visited, their sections measured and, in many instances, sampled. Elevations were obtained barometrically and approximate locations sketched on a small-scale map. In a field where the coals are so well opened, the reconnoissance method gives a very fair idea of the number and character of the principal beds and their relative positions, and affords much evidence for their correlation over wide areas, without permitting the more refined work required to discover all the seams of the measures and to determine the details of geologic structure.

Feb 1, 1912

By Sidney Snook

FLUORSPAR production is the most important industry in a compact area in southern Illinois and western Kentucky bordering the Ohio River. Producers' activities do not usually figure much in the mining news of the country, so that few know that the last year or so has been an unusually active one. Mine shipments more than doubled in 1939 compared with the poor year 1938. The average price changed but little, though it is now about one-sixth higher than at the beginning of last year. The outbreak of war in Europe a year ago lent an immediate stimulus to the industry, though only about 15 per cent of the domestic consumption is normally imported, thanks to a tariff of $8.40 per ton, equivalent to about 30 per cent ad valorem. Be- cause of the increased production and many expansions and improvements in the mines and plants, the period since the beginning of 1939 has been the most important one for the industry in the last 15 years.

Jan 1, 1940

By F. W. Bowdish

Analysis of data on the equilibrium exchange of sodium ions from salt solutions for calcium ions, from various fractions of an oxidized calcareous iron ore from Lorraine, France, strongly suggests that the calcium may be attached to the solid by only one of its bonds. Nearly equal values were found for the equilibrium expression from data covering concentration ranges of 1000 fold for the salt and 235 fold for the ion-exchangeable calcium. Differences indicated between the exchangeable calcium contents of the slime and the sandy portions of the ore, as well as the equilibrium relationship itself, are of importance in the flotation of the ore. During an experimental program on the flotation of oxidized calcareous iron ores from Lorraine, France, ion-exchangeable calcium was found in the ore. Because this source of calcium ions, if not controlled, could thwart all efforts at flotation, an extensive study was made of the phenomenon. The part of that study reported here was to obtain data on the equilibrium established between ore solids and solutions of sodium chloride, and to analyze the data to try to understand better the physical chemistry of the exchange. The ore contains oolites of goethite and quartz grains embedded in a matrix consisting of calcite and a brown cement believed to be the residue from oxidation of the silicate minerals found in fresh unoxidized ore. When ground, a substantial fraction of the ore becomes a fine slime in which is concentrated more than half of the alumina content of the ore. It is believed that the alumina occurs as unidentified clay minerals with which most of the ion-exchange capacity of the ore is associated. A preliminary experiment on the exchange of ions from the ore for sodium ions from solutions of NaCl showed that calcium was about ten times as abundant as magnesium in the exchange solutions. Thus calcium was the predominant ion in causing difficulties with flotation, and it was the only one for which data was obtained in this study. It is believed that the omission of magnesium ion exchange from consideration does not invalidate the results. It is possible, however, that inclusion of magnesium in the analyses and calculations or its prior elimination from the samples would have improved the consistency of the results. EXPERIMENTAL Data about the equilibrium exchange of sodium from solutions for calcium from the solids were obtained using two different samples of material. The solids

Jan 1, 1963

By F. W. Bowdish

A theoretical and experimental laboratory study has shown that the rate of breaking of oversized particles in a ball mill is proportional to 1) the concentration of such particles, and 2) the area of the balls, provided that the balls are larger than a certain size relative to the particles. If all undersized material were removed as formed, the rate of breaking would be almost independent of the quantity in the mill. Rate equations are given which are similar to those for zero, first, and second order reactions. Deviations of small balls from the equation for a second order phenomena are quantified by a factor called "nipping efficiency." Some data are correlated by a dimension-less equation, which is used to estimate nipping efficiencies from data not in the correlation. The investigation described here was undertaken after a literature survey revealed that little was known concerning the mechanism of breaking of particles within a ball mill and the effect of this mechanism upon grinding rates. One paper, by Roberts1 , offered a theory concerning the mechanism of breaking, and a rate equation for the breaking of particles larger than some size to particles smaller than that size. That paper provided the starting point for a theoretical and experimental investigation of grinding under carefully controlled conditions. THEORETICAL CONSIDERATIONS In his paper on the probability theory of ball mill grinding, Roberts theorized that "... a given expenditure of power leads either to a certain number of point to point blows per bp-hr or to a certain distance of line contact per hp-hr ..." He assumed that the balls touch each other during each blow or during moving contact. Then he said that a volume of pulp, dependent upon the size being considered, would be covered per minute within which all oversized particles would be crushed to particles smaller than that size. Naturally, the higher the concentration of oversized particles in the pulp, the higher the rate of which they would be broken. From this reasoning Roberts obtained the differential equation -dC/dt = k hp/ton C (1) where k is a constant for any size of particle, density of particle, and moisture content of pulp. C is the percentage of oversize in the material to be ground, t is the time, and hp/ton is the power input per ton of material in the mill. He then integrated the equation to log Co/Ct = k/2.3 hp/ton t , where Co and Ct are the percentage of oversize at time zero and t respectively. By always using the same quantity of material in a mill and assuming that it required constant power to run the mill, he was able to combine the horsepower per ton factor with the other constants to give an equation for a first order rate.

Jan 1, 1961

By J. W. Mills

In 1956 the discovery of nickel on Jumbo Mountain, Snohomish County, Washington, focused attention on this part of the Cascade Range, far more renowned for its timber than for its mineral resources. Hand specimens assaying as high as 13 pct Ni encouraged Discovery Mines Inc. of Mount Vernon, Wash., to stake 12 claims in Township 31 North, Range 9 East of the Willamette Meridian. The property was leased to Climax Molybdenum Co. in January 1957. Trenching, sampling, and geologic studies were carried out during the late summer of 1957 when most of the snow had disappeared. Although the deposits are only about four miles south of the logging town of Darrington and about two miles. as the crow flies, southeast of the end of a good gravel road from that town, all camp supplies and equipment were air-dropped, owing to the extremely rugged nature of the terrain. GEOLOGY The rocks of Jumbo Mountain comprise a series of folded Tertiary sediments forming a belt one half to three quarters of a mile wide, trending northwest about parallel to the strike of the beds. This belt is sandwiched between two extensive in-trusives—gabbro on the northeast and quartz dio-rite on the southwest—and has been intruded by dikes of fresh and serpentinized dunite. Shear zones follow many of the dunite-sedimentary rock contacts, and in these the nickel mineralization is concentrated. A few transverse faults offset the sediments and ultrabasics. Sedimentary Rocks: Two kinds of quartzite make up the greater part of the sedimentary section. One is dark purplish gray, very fine-grained, and thin-bedded; the other is light gray to white, medium-grained, and well-bedded. Locally the light-colored quart lites contain grit and conglomerate horizons, rich in pebbles of white chert and very fine-grained quartzite. Intercalations of dark argillites near the summit of the mountain give many of the cliffs a striking banded appearance. Dark gray to black, aphanitic, thin-bedded argillites occur throughout the entire sedimentary belt. Beds vary from a few inches to a few tens of feet thick and some, near the summit, contain numerous fossile (willow?) leaves. Only the thicker beds were mapped. The sediments are quite fresh on the northeastern side of the belt and become more metamorphosed (hornfelsed) toward the southwestern side. Brown biotite is present in the metasediments in increasing amounts as the quartz diorite is approached. Near the intrusion, porphyroblasts of plagioclase, up to 1 in. across, testify to the soaking of sedimentary rocks by solutions emanating from the quartz diorite. Most of the sediments mapped lie along the southwestern limb of an anticline, the axis of which follows the crest of the mountain and plunges at a low angle to the northwest.

Jan 1, 1961

By J. B. Clark

In multiphase ternary diffusion studies, plots of the variation bf the composition on the isotherm constitutes one of the most effective methods of presenting experimental results, especially if such plots are made in a manner which relates the composition path on the isotherm with the diffusion layer structure in the couple. Unfortunately, if different conventions for plotting are used serious misinterpretations occur readily, causing apparent disagreement between investigators who actually share the same viewpoint. A common convention for mapping these diffusion paths is needed at this time because with the increasing use of the electron-probe X-ray microanalyzer, a much greater number of ternary diffusion studies can be expected in the near future. In an effort to prevent unnecessary confusion in the future litera- ture, a convention for these plots is proposed, as outlined below. A hypothetical example of the use of these conventions is given in Fig. 1 where the path of composition through the diffusion structure of the 100 pct A/50 pct B, 50 pct C couple is plotted on the appropriate isotherm of the ABC system. The lower case letters relate the region in the diffusion layer structure to the appropriate composition on the ternary isotherm. 1) The diffusion path is plotted on the isothermal section corresponding to the diffusion temperature of the couple. 2) The terminal compositions of the plotted diffusion path are the initial compositions of the couple halves—provided infinite boundary conditions are maintained. If, in either couple half, infinite conditions are not maintained, then the path terminates at the composition of the exterior surface of the couple. If, at this surface, the composition varies with time or if the plotted path is time dependent, then the diffusion time should be noted beside the plotted path. 3) A solid line crossing a single phase field (e.g., line a-b in Fig. 1) denotes an existing layer of that phase in the diffused couple. 4) A dashed line crossing a two-phase field parallel to the tie lines (e.g., line g-h) represents an interface between the two phases with interfacial compositions designated by the ends of the tie-line. The line represents no spatial extent. 5) A solid line crossing a two-phase field so as to cut tie lines (e.g., line b-c or line j-k) represents a locally equilibrated columnar two-phase layer. The solid line should cut those tie lines which correspond to the lateral interfacial equilibria along the columnar

Jan 1, 1963

By E. D. Gardner

IN 1947 the metal-mining industry . passed through a year of readjustment; catching up on development work has caused production to suffer. Skilled labor has been short in most mining districts, notwithstanding the highest wage rate paid in the history of the industry. The trend has continued toward increased mechanization and refinements in practices and methods to increase the tons produced per man-shift. Improvements in procedures, however, have not kept pace with rising labor rates; and, in general, labor costs per ton mined have steadily increased since the war years. Prices of base metals have been the highest in a generation, but most producing companies can afford to pay the high wages. Capital expenditures have been approved for improvements to increase the output per man, both to reduce unit labor costs and to increase output. Surveys indicate a continuing

Jan 1, 1948

By Henry Rawdon

THE following note describing the behavior of copper under rather unusual conditions is offered here for its suggestiveness rather than as a complete study of the question. The examinations described were made because of a request for information concerning the embrittlement of copper when heated in a molten salt bath (sodium chloride) for the purpose of cleaning it, as well as for softening it. It is well known that metals may be rendered very brittle by electrolytic action, in aqueous solutions, in all probability by the action of nascent hydrogen, and it was suspected that perhaps the embrittlement of the copper by means of the molten salt was produced in a somewhat similar manner. It was found that the copper was in contact with iron (or steel) while immersed in the molten salt, through the occasional use of an iron stirring rod, iron forceps for handling the pieces, and an iron pot for containing the fused salt. In the electrochemical potential series iron and copper stand some distance apart, copper being electronegative to the iron. Assuming that the two metals bear a similar relation to each other, when immersed in a bath of molten salt, as they do in an aqueous solution, they would be expected to form a galvanic couple, the copper being the cathode. By this means the copper might be embrittled, as often happens in aqueous solutions, by the action of the liberated hydrogen. In this case, however, the embrittlement must be attributed to some other agent than hydrogen. To demonstrate how copper may be embrittled under these conditions, two small rods, one of copper and the other of mild steel, approximately 3/8 in. (9.5 mm.) in diameter, were immersed in a bath of sodium chloride that had been heated somewhat above its fusion point (melting point of sodium chloride is 819° C.) and an electromotive force of approximately 6 volts from a storage battery was impressed upon the system. The copper was made the cathode and the action was continued for

Jan 2, 1920

By D. H. Trollope

In engineering in general, close agreement between theoretical predictions and structural performance is rare—this is particularly true in rock slopes. Since the complexity of natural arrangements makes exact theoretical solutions of associated structural problems almost impossible, the role of theory should be that of developing guides or markers to which observations and experience can be related. The author in this paper has outlined the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Some important practical considerations result—especially in regard to horizontal stresses—when theory is compared with full-scale experience. In the field of engineering activity, specific examples of close agreement between theoretical prediction and structural performance are rare. Particularly is this so for the case of rock slopes, where, owing to the complexity of the natural arrangements, it is quixotic to expect exact theoretical solutions to the associated structural problems. The role of theory is rather that of developing signposts or guide rails to which observations and experience can be related. It is with this in mind that the present paper has been prepared; the author's aim has been to set out briefly the results of a theoretical study of highly idealized models which represent both granular materials and jointed rock. Despite the idealization of the problem, it will be seen that the theoretical conclusions are in accord with full-scale experience, particularly as far as horizontal stresses are concerned, and they point to some important practical considerations. CLASSIFICATION OF ROCK SLOPES At the risk of over-simplification, an attempt has been made to classify the problem of rock slopes into three broad categories with respect to internal stress systems. These are illustrated in Fig. 1. It is tacitly assumed in this classification that the strength of individual particles is very much greater than the interparticle strength whether the particles are the crystals of an igneous rock (Case I) or the blocks of Cases 2 and 3. The Homogeneous Monolith: This case is representative of uniform unjointed rock. Under relatively low stress conditions the internal stress system may approximate to that of an elastic body as given by Terzaghi.' It is more usual, however, for overall stability, to consider the material as a rigid plastic which yields in shear when S =C + c tan 4> where S is the shear yield stress, o is the normal stress on the surface of failure, and C and d are empirical constants according to the Mohr-Coulomb criterion of failure. Sokolovsky has recently developed, for the first time, a series of mathematical solutions to problems involvinga C, mass subject to self-weight. He demonstrates that for such a case a semi-arch (Fig. 2) is stable. A corollary of this argument is that for a true C, d material a curved overhanging slope is possible and such an observation may well aid field identification of these materials. The shape of the curved slope face is however directly dependent on the C-value, and from the long-term point of view this is a most difficult value to establish with any degree of confidence. It is customary to measure C and 0 in some form of shear test—usually a triaxial compression test—on core specimens sampled from the rock, and as far as the author is aware the present case is the only one in which, as far as overall stability is concerned, such tests are

Jan 1, 1961

By AIME AIME

T HE 121st meeting of the Institute held in New York City, February 16 to 19, 1920, was a great success despite vicissitudes of weather of unusual severity. On account of tremendous snowstorms, only two members of the Canadian contingent arrived, and several of our members from the west arrived thirty hours late. Two weeks prior to the meeting, the heaviest snowstorm in 34 years wrecked the surface transportation in New York; and it was only by special dispensation that arrangements were effected, with the New York Street Cleaning Department to clear away 39th street in front of this building so that vehicles could reach the curb. The total registration of members and guests was 1138.

Jan 1, 1920

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