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By J. A. Herbst, D. W. Fuerstenau

The effect of mill speed and ball load on the dry ball milling of dolomite is examined in the context of the batch grinding model. Observed changes in the parameters of the model are interpreted, as far as possible, in terms of the mechanics of particle motion in the mill. A parameter estimation scheme previously proposed by the authors is shown to provide the basis for a successful simulation of grinding behavior over a wide range of mill speeds and ball loads. Finally, a combination of experimental and simulated results is used to determine the optimum mill speedball load for closed circuit grinding in this mill-material system.

Jan 1, 1973

By Robert C. Bolger, John H. Weitz

REFRACTORY clay, one of Pennsylvania's important nonmetallic mineral resources, occurs at several horizons in beds of Pennsylvanian age. The Mercer fireclay, of Pottsville age (Table 1), is the most important of these clays. A study of this fireclay has been conducted by the Pennsylvania Geologic Survey discontinuously over a period of seven years. The work has included field mapping of a rather large area, as well as petrographic, differen¬tial thermal, and X-ray studies of the fireclay. A comprehensive report on the project is now in preparation.

Jan 1, 1952

By J. R. Long, E. L. Anderson, R. S. Dean, F. S. Wartman

TITANIUM has been estimated to comprise about 0.65 per cent of the earth's crust and ranks fourth in abundance among the metallic elements suitable for engineering uses. In spite of this, applications of titanium for structural purposes have not as yet been developed. Its commercial exploitation has been largely confined to the chemical industries and the production of paints and pigments; no doubt because of the difficulties that lie in the way of preparing the pure ductile metal. Published reports, however, indicate that ductile titanium can be prepared and possesses some unique properties. This, together with the occurrence in this country of several important titaniferous deposits, has led the Bureau of Mines to investigate processes for the production of metallic titanium, 'methods required for its fabrication, and the properties that may be produced in this interesting metal. METHODS OF PREPARING METALLIC TITANIUM Many early investigators claimed to have isolated metallic titanium; but in the light of present knowledge, it seems that they really had produced various mixtures of carbides and nitrides that have a metallic appearance but are brittle, hard, and unworkable. The first metallic titanium pure enough to be malleable when cold was produced by Hunter1 in the early part of the twentieth century. Kroll,2 van Arkel,3 and Fast,4 subsequently confirmed the facts that pure titanium is a ductile metal and that small amounts of impurities were responsible for previous reports of brittleness. When heated, titanium reacts chemically with various gases, such as hydrogen, oxygen and nitrogen; if the volume of gas thus absorbed is too great, the metal becomes brittle and unworkable. The principal difficulty in making ductile titanium is prevention of such contamination, and the success of a given process may be judged by the completeness with which it solves this difficulty in a practical manner. Of the gases mentioned, hydrogen is the least objectionable, since its absorption by the metal is completely reversible and, although dimensional changes occur and absorption of hydrogen embrittles the metal, the gas may be removed readily by heating in a high vacuum for a short time. On the other hand, the absorption of oxygen or nitrogen results in the formation of permanent 'solid solutions of the oxide and nitride, which cannot be decomposed by the strongest reducing agents2 with sufficient completeness to restore the inherent ductility of the metal. Because of

Jan 1, 1946

By Paul Billingsley

The Asientos-Tepezala district is in the north of the State of Aguasca-lientes, about 30 miles north of the city of Aguascalientes, the capital. The district is reached by a standard-gage railway on the west side through the junction, Rincon de Romos, which is on the main line of the National Railways of Mexico from El Paso to Aguscalientes. The terminal is Tepezala. On the east side a narrow gage connects Asientos with the junction, San Gil, on the main line, Asientos to San Luis Potosi. Tepezala on the west side of the Asientos hills is about 2 miles from Asientos on the east side. The area between the two mining centers is separated by a low subdued divide which forms the central part of the hills. The district is in a group of isolated hills surrounded by characteristic bolsón plains. The hills rise above the surrounding plains about 6500 to 10,000 ft.; the highest peak is Alta Mira. The two mining districts lie somewhat upon the flanks of the hills at about the same elevation, 7200 ft. The district is an old one and has been known since early in the 17th Century when the mines were worked by the Franciscan Monks. Their mining operations, which were limited to the oxidized ore above the water level, consisted chiefly in extracting silver from the Santa Francisca vein. To judge from the old workings and the remains of surface plant, the operations were on a large scale. By modern mining operations since about 1900, the various mines of the district have been one of the principal sourees of ore for the smelter located at Aguascalientes. Topography The topographic features of the Asientos hills are largely controlled by the character of the underlying rocks. During the Tertiary period, the entire group of hills was probably covered by extrusive volcanic material in the form of cones and lava flows. The central part of these have since been carried away by erosion, so that remnants have been left along the borders of the hills. These remnants form rather conspicuous peaks,

Jan 1, 1927

By Warren J. Jackson, John L. P. Campbell

Automatic recording of the radioactivity of the earth's formations provides a log of relative intensities that, if properly interpreted, can be applied to oil-field engineering. Production, engineering, and geological departments regard the radioactivity log as a forward step in the securing of more conclusive information for successful well completions. Explanations of the technique, together with some of the problems to which radioactivity logging have been applied, are presented in this paper. Introduction Those responsible for the completion of new oil and gas wells, or with planning workover operations on old wells, have followed closely the development of radioactivity well logging because they are interested in reducing the number of unknowns that usually are present in such work. Many operators have made use of the log, or are acquainted with at least one of the applications, but it is unlikely that any one operator is familiar with all of the many applications that are possible. The purpose of this paper is to present a representative example of each of the many applications, wherever the information has been released by an operator, and to illustrate by hypothetical examples other applications, releases for which have not been given. In this way, it is hoped that a better understanding of the scope of this new engineering tool may be obtained. Athough the literature contains many references that describe in detail the theory, development, and application of radioactivity well logging, a brief discussion of the technique may be helpful to those who are investigating the subject for the first time, All rocks contain radioactive material in varying concentrations. In general, shales contain relatively more radioactive material than sandstones or limestones. These radioactive materials disintegrate with time into other materials of lower atomic weight, and in that process of disintegration the rocks are emitting many rays, the most penetrating of which is the gamma ray. The intensity of emission of the gamma ray is proportional to the quantities of radioactive materials present. A higher rate of emission would be observed, therefore, opposite a shale than opposite a sandstone or limestone. Since measurable intensities of gamma rays are capable of penetrating as many as five concentric strings of casing, and as the gamma-ray intensity is relative to the formations, the measurements of variations in gamma-ray intensities offer a means of identifying cased-off formations in their proper stratigraphic sequence. TEe Gamma-ray Curve The measurement of gamma-ray intensi ties is accomplished by means of an ioniza-tion chamber that consists of a heavy cylinder, about 3 ft. long, that contains two insulated electrodes and is Med with an inert gas under high pressure. Under normal conditions no current will flow through the gas when an electrical potential is set up between the electrodes, but when

Jan 1, 1946

By John L. P. Campbell, Warren J. Jackson

Automatic recording of the radioactivity of the earth's formations provides a log of relative intensities that, if properly interpreted, can be applied to oil-field engineering. Production, engineering, and geological departments regard the radioactivity log as a forward step in the securing of more conclusive information for successful well completions. Explanations of the technique, together with some of the problems to which radioactivity logging have been applied, are presented in this paper. Introduction Those responsible for the completion of new oil and gas wells, or with planning workover operations on old wells, have followed closely the development of radioactivity well logging because they are interested in reducing the number of unknowns that usually are present in such work. Many operators have made use of the log, or are acquainted with at least one of the applications, but it is unlikely that any one operator is familiar with all of the many applications that are possible. The purpose of this paper is to present a representative example of each of the many applications, wherever the information has been released by an operator, and to illustrate by hypothetical examples other applications, releases for which have not been given. In this way, it is hoped that a better understanding of the scope of this new engineering tool may be obtained. Athough the literature contains many references that describe in detail the theory, development, and application of radioactivity well logging, a brief discussion of the technique may be helpful to those who are investigating the subject for the first time, All rocks contain radioactive material in varying concentrations. In general, shales contain relatively more radioactive material than sandstones or limestones. These radioactive materials disintegrate with time into other materials of lower atomic weight, and in that process of disintegration the rocks are emitting many rays, the most penetrating of which is the gamma ray. The intensity of emission of the gamma ray is proportional to the quantities of radioactive materials present. A higher rate of emission would be observed, therefore, opposite a shale than opposite a sandstone or limestone. Since measurable intensities of gamma rays are capable of penetrating as many as five concentric strings of casing, and as the gamma-ray intensity is relative to the formations, the measurements of variations in gamma-ray intensities offer a means of identifying cased-off formations in their proper stratigraphic sequence. TEe Gamma-ray Curve The measurement of gamma-ray intensi ties is accomplished by means of an ioniza-tion chamber that consists of a heavy cylinder, about 3 ft. long, that contains two insulated electrodes and is Med with an inert gas under high pressure. Under normal conditions no current will flow through the gas when an electrical potential is set up between the electrodes, but when

Jan 1, 1946

By Niels Hansen

Dispersion-strengthened aluminum products consist of an aluminum matrix containing finely distributed ceramic or intermetallic particles. Examples of the two types of product are SAP, in which the dispersed phase is aluminum oxide, and materials made from atomized aluminum alloy powder, in which the dispersed phase can be FeA1, particles.' A fundamental difference between the two types of product is that the elongation of aluminum/aluminum oxide products decreases with increasing temperature, whereas the elongation of aluminum- FeA13 products, like that of aluminum alloys, increases with increasing temperature. As regards the structural stability, aluminum/aluminum oxide products are stable to temperatures above 600° C as aluminum oxide does not react with aluminum, whereas prolonged heating at above 400°C of aluminum-FeA1, products leads to coarsening of the intermetallic phase and loss of strength.' On the basis of these results it is supposed that a dispersion-strengthened product combining strength, ductility, and stability at elevated temperatures may be obtained if the dispersed phase reacts with the matrix in such a way that the reaction does not proceed at any significant rate at the application temperature. Different ceramic or intermetallic compounds may be selected as the dispersed phase, and, as alloying of the matrix phase may also influence the reaction, many possibilities exist for each metal. In the present study, aluminum products containing different oxides have been examined. For a reaction to take place between the dispersed oxide and the aluminum the free energy of formation of the oxide (MeO) must be greater than that of aluminum oxide; the difference should, however, not be too great in order to limit the reaction rate. Furthermore the aluminum alloy formed when aluminum reacts with the dispersed oxide should have a melting point near

Jan 1, 1969

By William G. Pariseau

There are important phenomena in rock and soil mechanics that cannot be explained in terms of theories of homogeneous, isotropic materials. Subsidence of strata about mine openings is an example. In-situ stress measurements in nonisotropic sedimentary and metamorphic rocks is another. Patterns of joints, faults, fractures, and similar geologic features impart directional mechanical properties to rock masses that are locally isotropic or anisotropic. On the geologic scale, the nonhomogeneity of composite rock masses may, in certain instances, be dealt with as homogeneous anisotropy. The mechanics of large rock masses can, therefore, be expected to involve considerations of anisotropy. The source of the anisotropy is not relevant. Once the scale of observation is selected and the material is defined accordingly, the analysis of stress and deformation proceeds without regard to the numerical values of the material constants. There are also important phenomena in rock and soil mechanics that cannot be explained in terms of linear elasticity, theory. For the mechanical description of anisotropic geologic materials capable of deforming beyond the limit of purely elastic strains, a plasticity theory is required. The purpose of this chapter is to present a plasticity theory for anisotropic rocks and soils. The proposed theory is based on the work of Hill in anisotropic metal plasticity and represents an extension of his work so as to include anisotropic geologic materials. The point of departure from metal plasticity theory begins with the inclusion of the normal stresses as linear terms in the yield condition, which plays a central role in plasticity. Once the yield condition is established, the plastic strain increments are obtained immediately through the principle of normality. For practical applications, some simplification of the three-dimensional theory is re-

Jan 1, 1972

BRADEN, the most southerly of the three big Porphyries in Chile and the first to start production (in 1910), is a remarkable mine. It would be interesting to know just how much it has contributed, and will contribute, to the earnings of the Kennecott Copper Corporation, which acquired 95 per cent of Braden stock in 1915 by an exchange of shares and which subsequently obtained the remainder. Because of this complete ownership no separate annual report is published (as is the case with Anaconda's South American subsidiaries, Chile and Andes). Income, taxes, operating costs, earnings, and other financial data, including the balance sheet, are consolidated with corresponding items applying to Kennecott's manifold operations in the United States and other foreign countries. If Braden were in the United States it would be possible to arrive at a pretty accurate estimate of revenue realized each year from the sale of copper simply by applying the average published market price to the production as reported by the company. However, because of the restrictions on sales imposed by the Chilean Government and the almost fantastic regulation of exchange rates in the past, no estimate of the sort would be reliable. This point is illustrated by the following comparison made by Charles R. Cox, president, in Kennecott's report for 1955: In each year, 1954 and 1955, Braden supplied about 30 per cent of Kennecott's total copper deliveries; but Braden's operations contributed 16.7 per cent of consolidated net income in 1955 against only 6.2 per cent in 1954. More will be said later about exchange rates, taxes, and restrictions, and the recent improvement in the situation. Of course another element of

Jan 1, 1957

By Morris Cohen

It has been known for several years that in certain age-hardenable alloys precipitation of finely divided particles occurs simultaneously with the changes in physical properties; while, in other alloys, these changes take place prior to, or without any, precipitation. The silver-copper alloys are generally considered to be the classical example of the first group, and the aluminum-copper alloys (duralumin) are typical of the second group. The two types of aging are explained by the precipilation theory and the knot theory respectively.‡ It is well recognized now that these theories do not conflict with each other; the one used for a given aging system depends upon which way the alloy in question happens to age-harden. However, previous work on the aluminum-copper al1oys1,2 has shown that if the aging temperature is raised sufficiently the hardening will be accompanied by actual precipitation. In fact, it is quite probable that all of the so-called knot-hardening alloys will harden by precipitation at elevated temperatures. Therefore, a combination of the knot and precipitation theories is necessary to give a complete picture of the agehardening of these alloys, and indicates that knot formation and precipitation are not independent processes. To test the generality of this concept, it is necessary to show that the alloys that commonly harden by precipitation will harden prior to precipitation if the aging temperature is sufficiently lowered. For this reason, it would be well to carefully re-examine the aging characteristics of the silver-copper alloys at aging temperatures somewhat below those used by previous investigators. If hardening can be detected prior to precipitation in these alloys, it will lend great weight to the idea that knot forma-

Jan 1, 1937

By Norman D. Fitz Gerald

The lack of a continuous operating balance in petroleum refining, which is analyzed in this paper, is by no means a feature solely of this division of the oil industry. Serious disequilibria of a capital as well as an operating nature exist both in the producing and marketing departments, while problems in the former and to some degree the latter are complicated by political involvements. Attention has previously been directed to the unstabilizing influence of present proration formulas in stimulating unnecessary drilling.' While equilibrium in petroleum refining operations has been fairly well maintained in the past decade, examination of departures may prove fruitful. Economic analysis is the application of time and motion study to the functioning of management, rather than labor. Properly applied it may reveal changes in policies that would increase the utility of the properties and facilities of the industry for stockholders, employees and the public, while contributing a stabilizing influence to the general economy. The study of economic equilibrium is essentially one of measurement and interpretation, requiring adequate data and the development of a technique of analysis that employs statistical and mathematical methods as a supplement to the broad descriptive phase of economics. Economic equilibrium in petroleum refining is a dual concept. It embraces both the over-all balance between total storage and total demand for major products and the internal balance between the demands and inventories of the various products. The latter is the more complex of the two for it is concerned with proportionating the supplies of the several products stemming from the joint source to the demands for the individual products which are subject to wide variations. All the products are essentially nondurable goods, and they are used both by producers and consumers but in varying proportions. Motor fuel is very largely a consumer's good, while residual fuel oil is almost entirely a producer's good, the other products falling between these extremes. The peculiar-

Jan 1, 1939

By Norman D. Fitz Gerald

The lack of a continuous operating balance in petroleum refining, which is analyzed in this paper, is by no means a feature solely of this division of the oil industry. Serious disequilibria of a capital as well as an operating nature exist both in the producing and marketing departments, while problems in the former and to some degree the latter are complicated by political involvements. Attention has previously been directed to the unstabilizing influence of present proration formulas in stimulating unnecessary drilling.' While equilibrium in petroleum refining operations has been fairly well maintained in the past decade, examination of departures may prove fruitful. Economic analysis is the application of time and motion study to the functioning of management, rather than labor. Properly applied it may reveal changes in policies that would increase the utility of the properties and facilities of the industry for stockholders, employees and the public, while contributing a stabilizing influence to the general economy. The study of economic equilibrium is essentially one of measurement and interpretation, requiring adequate data and the development of a technique of analysis that employs statistical and mathematical methods as a supplement to the broad descriptive phase of economics. Economic equilibrium in petroleum refining is a dual concept. It embraces both the over-all balance between total storage and total demand for major products and the internal balance between the demands and inventories of the various products. The latter is the more complex of the two for it is concerned with proportionating the supplies of the several products stemming from the joint source to the demands for the individual products which are subject to wide variations. All the products are essentially nondurable goods, and they are used both by producers and consumers but in varying proportions. Motor fuel is very largely a consumer's good, while residual fuel oil is almost entirely a producer's good, the other products falling between these extremes. The peculiar-

Jan 1, 1939

By E. H. Bronson

PROPERTY of Malartic Gold Fields Ltd. is situaated in the great clay belt in the northern part of the Province of Quebec. This belt represents the floor of the glacial lake Barlow-Ojibway. The clay blanket has a gently rolling, almost flat surface, with here and there projecting knobs and ridges that outline the large irregularities of the surface on which the clay was deposited. At irregular intervals glacial eskers dominate the landscape. The ore-bearing country rock is covered by strata of clay, sand, and silt to a depth varying to 40 ft. There are serious structural problems when it is necessary to place loads of unequal intensities on this surface to support buildings and machinery for a modern mining plant. Earlier mining companies and their engineers paid little attention to the science of soil mechanics, partly because they believed it unnecessary and partly because they knew little of the subject. The results are evident in some of the tottering structures in older camps. Careful analysis of soil problems is well worth-while, since cost of foundations may vary from 20 to 50 pct of the final cost of a structure. Low operating and maintenance costs can be achieved only in this way.

Jan 11, 1957

Conservation and Survey Division, University of Nebraska, Lincoln, Nebr. G. E Condra, State Geologist. Publications in geology of tlie Conservation and Survey Division are as follows: No 1, Stratigraphy of the Pennsylvanian System in Nebraska, by G. E Condra, 75 cents; 3, Correlation of tlie Pennsyl-

Jan 1, 1933

By William J. Coulter

WITHIN the past thirty years the United States has been involved in two tragic, vicious, and costly world wars. To make the world safe for democracy was the reason given for our participation, but the confusion and misunderstanding that prevails all over the world today suggests that war is not the proper approach to the attainment of that utopia. These conflicts were conceived and prosecuted by nations far advanced in civilization and culture. Their best manhood was sacrificed, a staggering tax burden was saddled on their peoples, huge financial losses were incurred, destruction of property was appalling, and cultural and peaceful scientific advancement received a setback that may require centuries to retrieve. Therefore, some basis is established for the conclusion that progress in the past fifty years has been most outstanding in the development of instruments used for death and destruction, and that progress in this direction between the two World Wars would indicate that the next war will go far toward total destruction of world civilization.

Jan 1, 1946

By D. R. Shreve, L. W. Welch

An analysis for predicting the behavior of reservoirs exploited by a combined gas drive and gravity draintrge mechanism is presented. The method allows the prediction of gas-oil ratio, oil production rate, and cumlulative oil recovery for high relief pools in which pressure is maintained either by gas injection in the crest of the structure or by a combined gas and water injection program. The reservoir is represented by a model of communicating vertical prisms, with production or injection at the upper or lower boundaries of each prism. The theory of macroscopic gravitational segregation of two fluids within a reservoir is discussed in detail for all ranges of saturation. A description of an application of the analysis to a typical field problem is also presented. INTRODUCTION The importance of gravity drainage as a producing mechanism has become more evident during recent years. However, many of the reservoir engineering methods which have been used in the past for predicting the behavior of reservoirs producing by this mechanism have required such drastic, simplifying assumptions that the calculated performance in some cases does not resemble the actual pool behavior. The mechanism of fluid displacement in porous media has been described by Buckley and Leverett,1 and a simplified "one zone" method based on this development has been used by engineers to evaluate the performance of gravity drainage pools. Welge2 has modi- fied this approach so that the calculation time has been markedly decreased. In addition, many other authors3-9 have analyzed various phases of the gravity drainage producing mechanism during the past several years. In a high relief reservoir in which gravity may affect the recovery mechanism, there are two main types of exploitation programs which can be employed: 1. Reservoir pressure is maintained by injecting gas into the upper portions of the reservoir. In this case gas is not released from solution and, if dynamic pressure drops are small compared to the total pressure of the system, the gas and oil may be considered to be immiscible and to have constant fluid characteristics. 2. Reservoir pressure is not maintained and a "natural depletion" mechanism prevails. The term "natural depletion" can be used to describe the production history of a reservoir in which a gradual decline of average pressure and the associated release of solution gas continue throughout the producing life. In this mechanism gas is released throughout the reservoir and there is a continuous change in the characteristics of both the gas and the oil phases. It is the purpose of this paper to present the results of mathematical developments by which a method has been devised for evaluating the performance of reservoirs which are depleted by the first type of exploitation program discussed above. It should be mentioned that, although throughout the analysis gas and oil represent the two fluids existing in the reservoir, the method is equally applicable to gravity drainage in water-oil systems. STATEMENT OF PROBLEM In reservoirs of pronounced structural relief, where the closure of the oil section is great or the angle of

Jan 1, 1957

By Fred C. Bond

IN crushing and grinding the larger particles are more exposed to the work input. They absorb most of the work and protect the smaller neighboring particles from destructive contact with the crushing surfaces or grinding media. The importance of this exposure differential upon the reduction efficiency and product size distribution has long been recognized. Unfortunately, there has heretofore been no direct method of evaluating it, and such indirect methods as observing the slope of the plotted product size distribution line have been used as an indication. In this presentation the Third Theory of Comminution1 has been used, together with the exponential formula for size distribution, to evaluate the exposure ratio and exposure constant and to illustrate examples of their utility in crushing and grinding applications.

Jan 12, 1957

By Arthur C. Spencer

In extension of a suggestion already made to account for certain features observed in the Juneau gold-belt in southeastern Alaska,' it is the object of the present paper to indicate in detail certain conditions in which deformation of rocks under their own weight might lead to the production of fractures in which veins could be deposited. A direct, uniformly-distributed pressure of sufficient intensity, applied to an elastic brittle mass offering strung resistance to deformation, produces rupture. In a material of ideal properties the surfaces of rupture under such pressure would be shearing planes inclined at 45' to the line of force, unless there be preliminary deformation, in which case this angle would be greater than 45. This general conclusion, resting upon analytical mechanics, is completely supported by the results obtained by DaubrBe2 in experiments upon the deformation of wax and resin prisms under compression. Let us then first consider one of Daubree's diagrams. In the case illustrated in Fig. 1, four sets of fractures in two approximately right-angled pairs (that is to say, in conjugate sets) were produced by endwise compression of a square cross-sectioned prism. These fractures cut the axis of compression at approximately equal angles, not varying greatly from 45o. The location of the four sets of fractures is obviously determined by the shape of the prism, since the material in each corner acts in a way as a buttress, permitting the bulging to take place most readily on the sides. By limiting the directions in which bulging may take place, results of a more simple nature could be obtained. Take, for instance, a square prism, and place it between two fixed and

Jan 1, 1906

By William Fink

ALTHOUGH age-hardening in an aluminum-base alloy containing magnesium was observed by Alfred Wilm1 as early as 1911, it was not until 1919 that a theory of the mechanism of age-hardening was proposed. Merica, Waltenberg and Scott,2 studying the age-hardening character-istics of Duralumin at the National Bureau of Standards, came to the conclusion that age-hardening of this alloy is caused by the precipitation of CuAl2, which is less soluble at the aging temperature than at the solu¬tion heat-treating temperature. It was postulated that the initially precipitated particles were of fine colloidal dimensions but that they gradually grew in size. Maximum hardness was assumed to be attained when the particles reached a critical size. This theory was at first received skeptically, since it was a widely accepted view at that time that the solid solution state should represent the hardest state of an alloy. Shortly thereafter, Jeffries and Archer proposed their well-known "slip interference theory."3 They suggested that age-hardening was accomplished by the precipitated particles acting as keys interfering with slip along crystallographic glide planes. They showed that this mechanical theory led directly to the assumption that maximum harden-ing would be produced by particles of a critical size, which they suggested would have a diameter approximately 10 times that of the aluminum atom. This contribution amplified and explained so rationally the age-hardening theory of Merica, Waltenberg and Scott that wide accept-ance resulted.

Jan 1, 1939

By R. H. McLean

Jet impingement produces two mechanisms to clean the bottom of a borehole during jet-bit drilling operations. One is an impact-pressure wave in the immediate area of jet impingement. The other is crossflow, which spreads across the bottom away from the pressure wave. Measurements of the vertical distribution of the cross-flow at several positions beneath a 4 3/4-in. tricone jet bit in a laboratory model show that the maximum velocity in the crossflow is directly proportional to the square root of the product of the rate of flow and the velocity of the jets through the nozzles (QV). Other measurements in the laboratory model show that gradients in the impact-pressure wave are directly proportional to the jet QV if the diameters of the nozzles are held constant. Consistency of the basic relationships through changes in the Reynolds numbers of the jets from 31,000 to 93,000 suggests that the laboratory results should be representative of typical flow in field operations having higher Reynolds numbers. Estimates of the impact-pressure waves under conditions other than those in the jet-bit model may be made by comparison with a less complex model—impingement of a jet against an unrestricted flat surface normal to the jet. Equations derived from current jet technology describe the wave in this simple system for a wide range of conditions. INTRODUCTION The efficiency of rotary drilling operations is strongly linked to the efficiency with which cuttings are removed. Cuttings remaining on the bottom of the borehole will impede further penetration by the bit until they are removed. Wasteful regrinding is prevented if the fluid circulated past the bit removes cuttings as rapidly as they are made. Most investigations of bottom-hole cleaning under bits have been concerned with the rate-of-penetration effects of bit type, nozzle configuration, fluid properties, pressure gradients and utilization of hydraulic horsepower. These investigations have shown that drilling muds, weighted to keep the pressure in the borehole greater than in adjacent formations and carrying material which forms a filter cake, apparently plaster cuttings against the bottom, making them difficult to remove. In addition to a demonstration of the factors causing poor cleaning, the most significant result of these previous investigations has been the increased use of jet bits accompanied by better hydraulic programs and better selection of drilling fluids. Undoubtedly, these practices have improved bottom-hole cleaning, but rates of penetration when drilling with muds are still often lower than would be expected with perfect cleaning." Although there is general agreement with the concept that increasing hydraulic energy at a jet bit often increases the rate of penetration by improving cleaning, research workers have differed as to the best criterion for evalyating hydraulics. Some lean toward maximizing the product of the rate of flow and the velocity through the nozzles (QV) others prefer to maximize the hydraulic horsepower at the bit;'"-' "till another says that neither criterion is universally suitable."' This controversy shows that conclusive field evidence has not established the superiority of either of these criteria. Analysis of the fluid flow which cleans the bottom should contribute to resolving the controversy. Impinging jets clean the bottom by creating two mechanisms capable of dislodging cuttings. One is the impact from the momentum of the jet and the other is the flaw parallel to the bottom away from the area of impingement. The impact force appears in the form of a pressure wave on the bottom and, in this paper, is called the impact-pressure wave. The flow parallel to the bottom is called crossflow. Fig. 1 illustrates these two mechanisms. This paper describes crossflow and the impact-pressure wave beneath jet bits and relates them to controllable parameters. Through these relations, criteria for use in designing hydraulics to achieve maximum use of the mechanisms of cleaning are derived. PROPERTIES OF CROSSFLOW CONCEPTS DEVELOPED IN PREVIOUS INVESTIGATIONS Concepts of scavenging the bottom by crossflow have been well discussed by Bobo, et al." They examine the means by which crossflow may create forces on cuttings and conclude that the cleaning action of crossflow can be increased by increasing the velocity of the flow stream close to the bottom. Using boundary layer theory, they indicate that a reduction in the viscosity of the drilling

Jan 1, 1965