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By E. J. Quinn, M. F. Fogler

In a recent paper, Rawdon and Mutchlerl gave some exceptionally interesting results on the Brinell and scratch hardness of severely cold-worked metals. In their work, they found that, on continued cold rolling, the metal hardened up to a particular point and then reversed and became softer; this was true for both Brinell and scratch hardness values. The generally reported behavior2 of metals, with respect to Brinell tests on cold-worked material, is that the metals harden up to a certain point and then, on further cold rolling, no change in Brinell hardness occurs. Jeffries and Archer3 state that there is little difference between the scratch hardness of annealed and cold-worked metals; the work of Faust and Tammann4 also indicated no difference between the hardness of annealed and cold-worked copper. Rawdon and Mutchler found, when they plotted the reduction ratio (initial thickness divided by thickness after rolling) against the hardness value for the cold-rolled material, that the hardness number increased up to a reduction ratio of about 3 and then decreased and became even smaller than that for the annealed metal. This behavior was reported for both scratch and Brinell hardness; Figs. 1 and 2 show their results for Brinell hardness on the metals for which they published data. This is an exceptionally interesting phenomenon, if it occurs under all conditions of rolling, and would have an important bearing on the practice of cold

Jan 1, 1925

By P. H. Royster, T. L. Joseph

In a study of the blast-furnace process, the Bureau of Mines has made many experiments for the purpose of determining the exact nature of the combustion of coke in the neighborhood of the tuyeres. Two papers1 presented at a meeting of this Institute discussed somewhat the practical aspects of coke combustibility in its relation to the operation of the blast furnace. In a later paper,2 Sherman and Kinney discussed the possible effect of variations in the combustibility of cokes on the furnace operation, and find that the "reoxidation theory" of Koppers and the "heat concentration theory" of Brassert³ are insuffcient to explain the variation in the conduct of different cokes that has been observed by furnace operators. In their report to the D-5 Committee of the American Society for Testing Materials, with which the Bureau of Mines has been cooperating, Perrott and Fieldner4 seem to agree with Sherman and Kinney that, for practical purposes, the nature of the combustion of coke at the tuyeres of any furnace is constant and is affected neither by the physical properties of the coke nor by the nature of the furnace operation. They omit as unimportant any tests on the combustibility of coke from their proposed methods for standard tests on coke. In the last two papers, it is pointed out that performance tests, in which all other factors except coke quality are kept constant, are to be desired and

Jan 1, 1924

By P. Nelson, K. L. Gunsallus, A. R. Ingraffea, J. F. Beech

INTRODUCTION Fracture toughness, KIC, is an intrinsic material property and is a measure of the energy required to create new surface area in a material. Fracture toughness measurements can be made for a wide range of rock types (Ouchterlony, 1980). As a measure of energy of comminution, fracture toughness might be used for more sensitive predictions of Tunnel Boring Machine (TRM) performance than are possible with other index measures in current use. This paper describes part of an ongoing, comprehensive, analytical/experimental program aimed at evaluation of KIC in such a role. The program includes efforts to: 1. Provide a firm analytical basis for a test specimen geometry: the core-derived short-rod. 2. Develop simple, inexpensive testing equipment and techniques. 3. Evaluate the accuracy of the above by testing rock and other materials and comparing the measured fracture toughness with those obtained by other methods. 4. Measure fracture toughness of a substantial number of different rocks from three ongoing TBM projects. 5. Compare fracture toughness results with other strength measures. 6. Compare all test results with observed TBM performance in the three projects. Presented here are summaries of all but the last of these efforts. Comparative evaluation of KIC as a more senstive rock property for TBM performance prediction will be the subject of the oral presentation and a subsequent paper.

Jan 1, 1982

The following tables showing the output of coal during the year 1913 have been secured y R. H. Morris, of Pocahontas, Alberta, Canada, for the use of the Committee through the kindness of John T. Stirling, Chief Mine-Inspector of Alberta. The principal mining districts are, Crow's Nest Pass, Calgary, Lethbridge, and Edmonton, the outputs from which were as follows: Tons Crow's Nest Pass 1,849,435 Calgary...: 627,461 Lethbridge ; 966,020 Edmonton 863,430 Total 4,306,346 Of this quantity there was exported to the United States, principally from the Crow's Nest Pass district, 138,201 tons of 2,000 lb., that being the ton used throughout the Province. This production consisted of lignite, bituminous coal, anthracite, coking coal and coal used in making. briquettes, as follows: Tons "Lignite coal" (lignitic?) 1,763,225 Bituminous coal 2,374,401 Anthracite coal 168,720 Coking coal 104,012 Coke produced 65,167 Briquettes produced 130,861 The only district in which coke was made is the Crow's Nest Pass district, and the entire product was consumed in Canada. The total number of persons employed is as follows: Above ground 2,231 Underground 5,837 Total 8,068 The per capita production was as follows: Tons of coal mined per employee 533 Tons of coal mined per underground employee 737

Jan 7, 1914

The Institute published a collective index of- Volumes I to XXXV inclusive, which has been very extensively purchased and used by the members of the Institute. It enables one to look, up any subject in the first thirty-five volumes and is useful to those who have the Transactions, as well as to those who have not, because it tells what subjects have been treated and enables one to look these matters up in his own library and then afterward either to procure the individual papers from the Institute at the price of $1 each, or to procure Volumes, or to consult the Trans-actions at a nearby library, if such a one is available. It now seems desirable to publish another collective index, and the Editorial Department, upon the authority of the Board of Directors, has prepared an index of Volumes XXXVI to LV inclusive. This will be sold in the Institute's standard half morocco binding at a price of $5 and in paper covers at a price of $4. It wilt be ready in a few weeks. Those who already have the first index and purchase the second one, and those who purchase both, will have a complete index of the Transactions from Volumes I to LV inclusive. The Institute will be glad to receive advance orders for this index to insure prompt delivery upon publication.

Jan 8, 1917

By J. F. Nester, J. B. Schroeder

COMPOUNDS of rare-earth and iron-group elements are of technical interest because of their unusual magnetic properties. To date, however, all magnetic measurements1-4 have been made with polycrystalline, often polyphase, samples. For the measurement of anisotropic properties, single-crystal samples are necessary to avoid the averaging effect of randomly oriented grains. The purpose of this note is to describe a technique with which we have grown relatively large single crystals of YCo5, NdCo5, DyCo5, and "YFe9". Crystal growth of these materials is complicated because: 1) the binary equilibrium diagrams are, in general, not well-established; 2) in those cases where phase-equilibrium data are available, the compounds of interest are generally formed by peritectic reaction; 3) the molten component metals are chemically very reactive, making contaminaticn of the melts by the crucible material a serious problem. Techniques such as arc or levitation melting followed by strain annealing have been tried5)' in the past with these materials, but with little success because of the peritectic reactions and the inherently poor process control. For this reason we chose to use the zone-melting technique of Mason and cook7 for our work, since past workers8 have had some success in preparing single crystals of peritectic compounds by this method.

Jan 1, 1965

By L. W. Eastwood

THE structure of eutectics has been studied by a number of investi-gators, and the complexity of the structural relationship of the compo-nents has been agreed upon, especially that of the "eutectic colony," type III of Portevin's1 classification. This paper does not attempt to alter the present classifications of eutectics; rather, it discusses the relationship between the macrostructure and the microstructure of the copper-cuprous oxide eutectic, and describes in detail the mechanism of the formation and the structure of the eutectic. Further, throughout the entire discussion it attempts to point out certain misconceptions in regard to the interpretation of the observed structure of the copper-cuprous oxide eutectic, one of the so-called "eutectic colony" types, and to correlate as much as possible the work done by the writer with that done by other investigators. Of the three types of eutectics listed by Portevin,2 the eutectic colony type has presented the greatest difficulty in interpretation. Although the copper-cuprous oxide eutectic is typical of the eutectic colony type in appearance, it may not be truly representative because the copper forms about 96 percent of the eutectic and the cuprous oxide about 4 per cent. The interpretation of the origin and structure of the "eutectic colony" given here is strictly limited, therefore, to the copper-cuprous oxide eutectic.

Jan 1, 1933

By J. S. Kirkaldy, R. J. Brigham

AS part of a program to investigate the diffusive properties of dilute ternary austenites we have made a determination of the effect of chromium on the activity of carbon in ? iron. Samples of pure iron and Fe-Cr alloys were simultaneously equilibrated at 1000°C with atmospheres of controlled CO/CO2 ratio following the procedures of Darken and Gurry 1 and smith.' The 0.020 in. thick samples were analysed for carbon by microcombustion analyses3 to yield a set of isoacti-vity curves. The latter were converted to activity coefficient (standard state at infinite dilution) plots by combination with Smith's data2 for the activity of carbon in pure iron. Table I shows the compositions of the base alloys used while Fig. 1 shows the experimental results superimposed on a set of curves generated by the relation In?C=6.9NC- 10.7 Ne In the notation of wagner4 the interaction parameter is the second coefficient on the right, Sgr = - 10.7 This can be compared with a rather inaccurate value deduced from the transient equilibrium diffusion data of Kirkaldy et al.' as The authors are indebted to the American Iron and Steel Institute for financial support. This material is condensed from a B.Sc. Thesis submitted to Mc-Master University by R.J.B.

Jan 1, 1963

By Jackson R. Pellett

INTRODUCTION The Friedensville mine is situated in Upper Saucon Township, Le- high County, Pennsylvania, in the southern central part of the Allentown quadrangle of the United States Geological Survey, approximately 5 miles southeast of the City of Allentown and 4 miles south of the City of Bethlehem. Zinc was first discovered in the Friedensville area early in the 19th century and several mines were operating during the latter part of the century. Zinc oxide was produced in 1853 and zinc metal in 1859. All mining in the area ceased in 1893 chiefly because of an unfavorable economic situation caused by a severe ground water problem and competition from the higher grade ores in New Jersey. Property acquisition by the New Jersey Zinc Company began in 1899 and periodic exploratory drilling was carried on until 1940 when sufficient reserves were proved for development of a mine. Shaft sinking was undertaken in 1947 and, due to severe hydrologic conditions, was not completed until 1952. Production began in 1958 and today the mine is producing about 64,000 tons of zinc concentrate per annum. The concentrates are trucked to the Company's smelter at Palmerton, Pennsylvania, approximately 30 miles north of Friedensville. The mine also produces from its mill tailings industrial and agricultural grades of limestone for commercial markets.

Jan 1, 1970

By Carl Scholz

DURING November And December, 1907, Four Serious Mine-explosions Occurred In The Appalachian Coal-Field, Which Resulted In The Loss Of Nearly A Thousand Lives And Caused An Enormous . Damage To Property. These Accidents Attracted More Than The Usual Attention; Coal-Trade And Engineering Papers Contained Many Comments And Suggestions On The Cause And Prevention Of Accidents; The Daily Press In Many Instances Condemned The Coal-Operators And Charged These Accidents To Their Negligence, Or Their Anxiety To Make Money Without Adopting Precautionary Measures. Immediately After Each Accident The Respective State ..Authorities Ordered Close Investigations To Be Made, With The View Of Establishing The Cause And Suggesting Remedies To Prevent Recurrence. Representatives Of The Technologic Branch Of The U. S. Geological Survey, To Whom The Investigation Of Mine-Accidents Had Recently Been Delegated By The Secretary Of The Interior,. Visited The Mines And Co-Operated With The Local Authorities In Their Determinations. It May Be Safe To Say Here That An Investigation Of A Mine After An Explosion Has Occurred Discloses But Little, Because. The Causes Have Been Removed And Conditions Have Been Entirely Changed. On Jan. 8, 1905, The Coal-Operators Of West Virginia Organized An Association At Washington For The Purpose Of Making Extensive Investigations, And Sufficient Funds Were Pledged To Carry Out This Work. At This Organization Meeting, The Representatives Of The Geological Survey Present Had No Suggestions To Offer As To The Cause Of These Accidents. An Examination Of The Various Reports Concerning These Accidents Indicates That The Explosions Were Caused By The Ignition Of Gas Or Dust; They Show The Point Of Origin And The Direction In Which The Force Was Expended, And Give A Detailed Description Of The Damage Done. Very Little Has Been Said As To What

Jan 7, 1908

By G. W. LAAiIBOURNE

FEW mines possess a history of more fascinating interest than the Ontario at Park City, Utah. The famous Bonanza's production record of over $50,000,000; the great extent of its workings; the remarkable character of its mineralization; the fact that recent discoveries have shattered preconceived theories of the geology of the camp practically assuring the half-century old property a future as active and as prosperous as the past make the Ontario one of the unique mines of the world. A mere accounting of the wealth created by this historic property not only exemplifies the great profits

Jan 1, 1925

By C. W. Hall

MINE executives, as a rule, have always been willing to adopt new ideas of operation, or to listen to proposals which might increase the effectiveness of their enterprise, more especially so if they could be shown how definite results might be attained by introducing any conception suggested. In these days of high wages, high cost of supplies, and high taxes, operators are even more inclined to accord consideration to innovations or improvements, and many go so far as to employ men to conduct special investigations and make studies for the purpose of advancing production. Where a man is brought into an organization to do work of an efficiency nature, it often creates resentment among the operative heads because of having their work directly scrutinized, or investigated, and there is a tendency, if not actually to obstruct, to fa.il to cooperate; in which case the investigator is handi-

Jan 1, 1925

Jan 1, 1931

By G. W. Neighbor, M. S. Abrahams

The actice slip plane in InSb is found to be of the {111} type by using the method of two-tmce anulysis. Measurements of the rotation of the tensile axis with increasing plastic shear strain indicate that the tnacroscopic slip direction is a <110>. Recrystal-lization is first observed at a sheav strain of about 70 pct for a crystal deformed at a temperatzcre of 473° C and at a shear strain rate of 2.90 times 10- %ecc-I; the dislocation density corresponding to this value of the strain is 1 x 108 em-&apos;. At a shear strain of about 170 pct, the recrystallization process is complete. This appears to be the fimt time re-crystallization has heen observed in a semiconductor. V HE operation of the {Hi} glide plane in Ge was first noted by Gallagher.&apos; This finding was confirmed by Treuting who also extended the result to Si. Using X-ray techniques, Treuting3 demonstrated that the macroscopic slip direction in Ge was of the <110> type. The choice of the (111) <110> slip system in Ge is exected since in the diamond-type structure the {Ill7 plane is the plane of highest density and the <110> direction is the direction of closest packing.4 There is little reason to expect that the glide elements of InSb are different from those of Ge, since the zinc-blende structure characteristic of InSb is quite similar to the structure of Ge. With regard to InSb, Allen5 has indicated that the glide plane is the {111} type. There appears to be no quantitative determination of the glide direction, however. The present work was undertaken to establish both the glide plane and glide direction in InSb and also to see if recrystallization occurs at large shear strains. EXPERIMENTAL PROCEDURE Mechanical Deformation. The single crystals of InSb used in this investigation were deformed in uni-axial tension. The tensile axis of the specimens was [145] and the periphery was bounded by (111) and (321) planes as shown in Fig. 1. The metallographi-cally polished specimens were deformed in a dynamic atmosphere of He, using an Instron machine. The tensile tests were performed at temperatures in the range of 300°C to the melting point (525OC) and at shear strain-rates varying between 1.94 X 104 sec-&apos; to 1.94 x 103 sec-&apos;. Additional details concerning the preparation and deformation of the specimens have been presented previously.&apos; Analysis of the Glide Elements. The traces of the active slip plane in both (111) and (321) planes were analyzed according to the usual method of two-trace analysis." The macroscopic slip direction was determined by measuring the rotation of the tensile axis as a function of plastic strain,8 These measurements were made from Laue back-reflection X-ray photographs. The X-ray beam was perpendicular to the (111) plane. A given crystal was used for only one measurement of the rotation of the tensile axis after it had been strained to a predetermined value. Therefore, care was taken at all times to insure that the X-ray beam was parallel to the [Ill ] direction of all the samples. RESULTS AND DISCUSSION Glide Plane. After 3.4 pct plastic shear-strain, at a temperature of 369°C and a shear strain-rate of 1.94 x 104 sec-&apos;, the slip traces on the (111) and (3.21) planes appear as in Figs. 2(a) and 2(b), respectively. The results of an analysis of these glide markings demonstrate that the slip plane is (111). The operation of this plane is expected on the basis of the orientation of the specimen, since glide on this plane and in the [I011 direction will result in

Jan 1, 1962

By M. R. J. Wyllie, Walter D. Rose

The use of electrical well logs for the quantitative determination of such reservoir parameters as connate water saturation, formation permeability and connate water salinity has recently been attracting the attention of a number of workers1,2,3,4,5. While the theory of the determination of connate water salinity from the self potential S.P. log has received rather detailed treatment, relatively little attention has been paid to the theoretical aspects involved in the quantitative interpretation of resistivity data. It is clear that if electrical well logs can be used for the quantitative evaluation of physical characteristics of reservoir rock, they will provide a valuable tool to supplement cheaply information obtained by more laborious core analysis. In certain cases it is conceivable that the coring program could be considerably curtailed if the electric log could be relied upon to give reasonably accurate quantitative information. It is our object in this paper to examine the theoretical basis of quantitative log interpretation as expressed in such well-established logging concepts as formation factor and cementation factor. It is also our object to investigate the physical aspects of the rela- tionship which is presumed to exist between resistivity index and brine saturation in reservoir rock. In particular, we will endeavor to draw attention to the fact that it is possible to express these logging concepts in terms of capillary pressure-saturation relationships, permeability and tortuosity, parameters which we will consider in this paper to be fundamentally indicative of rock texture. The probability of being able to obtain from log recordings alone the data theoretically essential to permit quantitative log interpretatiou will be examined, and consideration will also be given to the problem of formulating simple semi-empirical relationships for use in the field. THEORETICAL CONSIDERATIONS The concept of formation resistivity factor, or as it is now commonly called, formation factor, appears to have been introduced by G. E. Archie",". Formation resistivity factor as defined by Archie is the resistivity of a rock 100 per cent brine-saturated divided by the resistivity of the brine. This relationship had previously been used by physical chemists and the concept is, for example, implicit in an early treatment by Fricke7 of the conductivity of aqueous slurries. Archie was able to establish the fact that although the relationship between formation factor and porosity did not change too greatly for different rock textures, the relationship between formation factor and permeability was markedly dependent on rock texture. The relationship found by Archie between formation factor and porosity was expanded by H. Guyod8. Archie had suggested that the formation factor, F, could be expressed in terms of the porosity, F, as follows: F =F-m .... (11 where, F = effective porosity fraction of the sand, and, m = an exponent greater than about 1.3. Guyod introduced the term cementation factor for the exponent, m, since it may be qualitatively shown that formation factor for any given porosity tends to increase as the sand becomes more cemented. It would appear that the concept of m as an exponent representing the cementation in a sand is strictly only of qualitative value, since the quantitative estimation of m by means other than the determination of F and F has not been possible. Guyod suggests that m can be estimated from a visual examination of a sample of rock, but this method appears to be both arbitrary and unreliable. It can be said, however, that in intergranular reservoirs of practical interest, the range of m is from about 1.4 to 3.0. A possible explanation for the fact that m is found to lie between these limits will be offered below. The determination of formation factor is an essential preliminary to the

Jan 1, 1950

By J. Chipman, J. C. Fulton

Reduction of Si from slag to carbon-saturated iron is a very slow reaction. The rate is nearly independent of stirring but is accelerated markedly by increased temperature. In a slag containing 45 pct SiO2, 38 pct CaO, 17 pct Al2O3, the energy of activation is approximately 130 kcal. AT temperatures of 1450" to 1600°C occurring in the hearth of the iron blast furnace, chemical reactions are normally expected to proceed with great rapidity. Many of the reactions of iron making are indeed quite rapid and attain a condition corresponding roughly to a state of equilibrium before metal and slag are tapped from the furnace. The one conspicuous exception is the reaction by which carbon in the coke or metal reacts with silica in the slag to deliver silicon to the metal. From the practical viewpoint the slowness of this reaction is indeed fortunate, for if it were fast enough to reach equilibrium during the time of contact, it would be difficult to produce pig iron of the desired low silicon content. The one other reaction which under certain circumstances can also be very slow is the transfer of sulfur from blast-furnace metal to slag. In their laboratory exeriments on this reaction, Hatch and Chipman found that at least 5 hr were required for the attainment of equilibrium in a small crucible and that the reaction was not accelerated by increasing the rate of stirring. Subsequently it was shown2 that the presence of a reducible oxide MnO greatly inhibited sulfur removal, and finally that SiO2 itself3 under some conditions has sufficient oxidizing Dower to interfere with sulfur transfer. The kinetics of sulfur removal are now rather well understood,4 and it has been shown3,5 that when the silicon content of the metal is high enough to prevent reduction of SiO,, the desulfurizing process is rapid. Thus the observations of slow removal of sulfur are associated with the coincident slow reduction of SiO2, a process which transfers both silicon and oxygen to the metal phase. It is, of course, the oxygen which interferes with sulfur removal. An explanation of the slowness of the silica reduction reaction has not been obtained. The sulfur transfer process has been shown by the authors5 to be at least partially transport-controlled in the absence of interference by silica. Under the experimental conditions. 99 pct of the total transfer at 1600" was accomplished within an hour. Under similar conditions the reduction of silica may not proceed half-way to equilibrium6 in 8 hr. It is scarcely imaginable that silica reduction could be transport-controlled when the slag contains 44 pct SiO2 and the metal about 1.4 pct C. The experiments reported here show definitely that it is controlled by a slow step or steps in the chemical reaction. One might expect to find such a slow step in the breaking of SiO bonds or in the slow removal of oxygen by carbon at the slag-metal or metal-crucible interface or by bubble formation. EXPERIMENTAL PROCEDURE The experimental procedure used in this investigation was similar to that used in the study of the kinetics of desulfurization.5 A sketch of the graphite crucible and stirrer used in the current work is shown in Fig. 1. The quantity of metal and slag used was adjusted so that the slag-metal interface was located between the top and bottom blades on the stirrer; the top of the slag layer was above the top blade. The stirrer shaft was hollow down to the metal level and served as thermocouple well or optical pyrometer target. Stirring speeds of 0 to 500 rpm were used. A carbon monoxide atmosphere was maintained in the furnace by flushing the gas over the slag surface, except in run No. 220 when it was bubbled

Jan 1, 1960

By Euclid P. Worden

In 1977, an article in World Mining1 reported a total of 2726 rotary blasthole drills in service. This figure included only those machines produced by three of the manufacturers building drills of this type. The total, therefore, is much higher. Rotary drilling in the mining industry is big business to the manufacturers and suppliers involved, and a significant cost item to mine operators. The time has come to take a hard look at rotary drilling technology with an eye to reducing costs by increasing drilling efficiency. The efficiency of any rotary drilling operation is best measured in terms of the rate of penetration achieved by the bit. In blast hole drilling, there are five factors which affect the rate of penetration. They are: (1) bit selection, (2) weight on the bit, (3) rotary speed, (4) hole cleaning, and (5) formation properties. Of these factors, all but one may be controlled by the operator. Looking at any one in detail may reveal possible improvements in the system. One of these factors -- proper hole cleaning - will be discussed in this paper. In order for a bit to perform at its maximum capability, each tooth or insert should strike fresh clean rock as it falls into its drilling position. If the tooth or insert lands on previously drilled cuttings, a major portion of the energy delivered to the bit is absorbed in redrilling this broken material. A major portion of the interest, therefore, should be directed to the proper cleaning of the bottom of the hole. In an in-depth study of the cleaning of large diameter holes, Allen2 reports that horizontal air velocities of 38.10 m/s are necessary to prevent the saltation of drilled cuttings on the bottom of the hole. The exact flow pattern on the bottom of the hole, however, is not generally known. The air leaves the bit through the jet nozzles and the mouths of the cones, but where it goes from there is uncertain. This problem should be investigated by the bit manufacturers because they can best utilize the results of such an investigation to provide a more effective product. Some work has been initiated in this area and competition will probably increase its intensity. Bailing velocity is the best criteria to measure the cleaning of the hole, including the bottom, and is the factor on which efforts toward improvement must be concentrated. The first consideration is "What should the bailing velocity really be?" In drilling deep holes for oil and gas, 15.24 m/s is the generally accepted figure. In blasthole drilling, the figures of 25.40 m/s for average rock to 35.56 m/s for iron ore were first mentioned by Capp3 in 1962. The recommendations are the same to this day. A number of questions could be asked in regard to the apparent disparity between these two sets of figures. Various investigators have derived formulas which support one or another of these criteria. A thesis on the subject was written by Alexander4 who derived a formula based on research which resulted in velocities in the lower end of the ranges quoted previously. He set out to compare this figure to laboratory tests and his tests indicated that the velocities given by the derived formula appeared to be high.1 Perhaps the best reason that the 25.40 to 35.56 m/s range has been used, is that these velocities seem to work. Below the accepted figures, low bit life and slow penetration rates occur. Above these figures, increasing amounts of abrasive wear on the drill pipe and stabilizers seem to appear. There is a fallacy to this entire approach, however. The entire velocity calculation is made using nominal bit and pipe sizes and compressor deliveries with no compensation made for losses in the system. Perhaps an examination of some of the things that are not presently considered could lead to some practical improvements in the operation.

Jan 1, 1980

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By Forrest F. Craig

Both early and more recent1 laboratory measurements of gas-oil relative permeabilities were made by subjecting oil-saturated cores to external gas drives. In these runs it was generally assumed that the flowing gas/oil ratio was constant at every point throughout the core. Using this assumption, the resulting equation for the gas-oil relative permeability ratio becomes A where Q is the flow rate at the producing end of the system. This relative permeability was then specified for the average saturation of the core. The assumption and resulting equation fail to recognize that in an external drive, the oil flow rate varies from zero at the injection end to a maximum at the producing end. The assumption also fails to consider the existence of a saturation gradient during an external drive. This saturation gradient is due solely to non-steady-state flow. Some authors2,3,4 have used this erroneous method of calculating relative permeability ratios from external drives. Other authors5,6,7 have used relative permeability ratios in calculating expected field performance by external drive, using Equation (1) and making the incorrect assumption that the saturation is uniform within the driven portion of the reservoir. To find the correct relation between the relative permeability. ratio at the average saturation and the produced gas/oil ratio, the insertion in Equation (1) of a factor, F, to adjust it for oil velocity gradient has been considered. The equation then takes the form Assuming that the oil velocity is directly proportional to the distance from the injection point leads to the conclusion that, for a linear system, the average oil velocity is one-half that at the producing end. Thus, the average gas/oil ratio is twice the produced gas/oil ratio, and Equation (2) is transformed into However, here again the existence of a saturation gradient is not recognized. The produced gas/oil ratio is related to the relative permeability ratio at the saturation of the outlet end of the system. It can be shown quite readily that, if the true log k,/k, saturation relationship is linear over small ranges of saturation, then d log kjko Where aaxv and u2 are the average and outlet saturations, respectively. Examination of Equation (3) shows that the factor F cannot have a single value over the whole saturation range. Another method of dealing with external drives is that of Buckley and Leverett.&apos; Their method, which assumes no gas expansion and outlet end effects, considers fully the saturation gradient present due solely to the displacement mechanism during an external drive, and applies Equation (1) to each point along this gradient. The calculation of production history using relative permeability ratio is straightforward. However, the calculation of relative permeability ratios from production history by this method is impractical. In a recent paper, Welge,1 using an approach similar to that of Buckley and Leverett, presents a simplified method for determining the saturation at the producing end of the system. At thi; saturation, the relative permeability ratio calculated by Equation (1) applies exactly, after breakthrough of the stabilizej front. By this method, relative permeability ratios or production history may be calculated with equal ease. Use of this method as a laboratory tool in determination of relative permeability ratios by external drive requires the knowledge of the total injected fluid volume; in addition to the average saturation and producing ratio. As a preliminary test of this method of calculation, laborntory external gas drives were run on a 3% in. diameter, 11 in. long sample of Nellie Bly consolidated sandstone. This core sample had a permeability of 824 md and a porosity of 28.1 per cent. The driving fluid was air. Three different oils were used, having viscosities of 1.4, 9.8, and 125 cp, respectively. The runs were made under identical pressure differentials,

Jan 1, 1952

By Cyril Stanley Smith

Jan 1, 1949