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With one shaft almost completed and another shaft being sunk, the scope of the Saskatchewan potash area is beginning to come into focus. Some 18 companies have reportedly leased more than four million acres to explore potash possibilities. PCA, farthest along, is located about 15 miles southeast of Saskatoon, and IMC has its project underway near Esterhazy in the eastern edge of the province. U. S. Borax and Chemical Corp. is also reported exploring the area. The field lies in the middle Devonian geological formation which was probed by oil companies along the 200-mile area across the province. Extensive examination began after World War II and deep drilling was started a few years later.

Jan 5, 1958

By M. P. Tixier, M. Gondouin, G. L. Simard

In the quantitative interpretation of the SP logs, the electrochemical component is generally taken equal to — K log Rm /Rw where K has the theoretical value corresponding to solutions of pure sodium chloride. This method may be misleading when relatively large quantities of salts other than NaCl are present in form-rrtion waters—as is generally the case for low salinities —or in gyp-base muds. In such cases recourse is made in the field to changing the K value or to adding a correction term to the equation on the basis of local experience. An investigation has been made in the laboratory of the influence of HCO3, SO4=, Ca++, and Mg++ on the amplitude of the SP deflection, which included in par-ricular determinations of the activity coefficients of Ca++ and Mg++. The theory, the experimental techniques and a tentative method for applying the results are described. So far, applications to actual field cases where chemical analyses of waters were available have provided an excellent confirmation of the proposed method. The case of the SP in very salty brines is also considered and it is shown that the use of activity data for sodium gives satisfactory results. HISTORICAL In early times of electrical logging, the SP curve was used exclusively as a tool for the location of permeable beds and the definition of their boundaries. Later, with the introduction of methods of quantitative analysis, attention was called to the possibility of deriving from the SP log some information on the formation water resistivity, which constitutes one essential element for the computation of water saturation from log data. The first laboratory experiments' in 1932 had shown that, as a result of electrochemical phenomena arising at the contact of the niud and the formation, the amplitude of the deflection of the SP curve was, at least partly, a function of the salt concentration of interstitial water and accordingly of its resistivity. It was indicated that the amplitude of the electrochemical component of the SP should be equal to K log R1/R2, R1 and R2 being the resistivities of the mud and of the formation water respectively. However, the exact value of the K coefficient was not determined at that time because the surface clay used for a laboratory model was far from an ideal shale membrane. Consequently, the way was not yet open towards quantitative interpretation. In the early forties, Tixier reported2, on the basis of field log observations, the following equation for the case of NaCl solutions, SP = -71 log f1c1/f2c2, c1 and c2 being the concentrations and f1, f2 the mean activity coefficients. The local variations observed in the empirical values of K, chiefly in the Rocky Mountains, led him to advance the opinion that, besides the relative amounts, the nature of the salts present in the solutions had a bearing on the magnitude of the SP. At about the same time Mounce and Rust- ad published laboratory results which emphasized the part played by the shale in the generation of the SP. On the basis of laboratory tests and theoretical considerations, Wyllie in 1948' published the following equation of the electrochemical SP for the case of NaCl solutions, SP= - 71 log (a1)m/(a2)m

Jan 1, 1958

By Kung-Lee Wang, Brian W. Mackenzie, Warren E. Morrison, DeVerle P. Harris, George F. Sharrard

The term "mineral economics" is applied to a wide range of activities in the mineral industries. Earlier chapters have described the application of economic concepts to the mineral industries-supply, demand, conservation, tariffs, etc. The solution of mineral economics problems is often assisted by the application of quantitative methods. The purpose of this chapter is to describe a number of quantitative methods-econometric, operations research, and management science techniques-which find application in the analysis of mineral economics problems. These methods include input-output analysis, trend analysis, forecasting techniques, simulation, multivariate statistical analysis, mathematical programming, and market research techniques. The purpose of this introductory section is to provide a mineral economics framework for the application of these methods. Mineral economics is a subdivision of economics that is justified by a sufficient number of economic problems in the mineral industry requiring special experience and an unusual combination of skills. These problems are concerned with the conversion of minerals as geologic resources to minerals as economic goods. The mineral conversion process is outlined in Fig. 8.A.1. The physical occurrence of mineral deposits in nature and the market demand for mineral products in the economy provide the basic stimuli. The conversion process embodies a number of sequential stages-exploration, the development of mineral deposits, and mineral processing facilities and, consequently, productive activity to supply market demand. Changes in demand and the depletion of deposits illustrate the dynamics of the process. Mineral economics applies economic con-

Jan 1, 1976

By D. B. Rushmore, K. A. Pauly

Of primary importance in mine-installations is the hoist, which has a very direct bearing on the successful operation of a mine. Conditions vary greatly with different mines, and especially in different localities. Such factors as depth, incline, the number of levels, permissible or desirable speeds, conditions of ore, etc., are always more or less special in each case. Veins of ore are never exactly duplicated, and the nature of the ground through which shafts are sunk may considerably modify permissible values. As mining-laws are made by the different States, they necessarily vary somewhat, and, even when not fully observed, they introduce factors which qualify the conditions of hoisting men and ore. The amount of timbering required is often of importance as relating to hoisting-conditions. Methods of loading ore affect the time required, as also does the question of the use of cars or skips. Safety-precautions must be very carefully considered, and the number of men in each mine, the number of compartments, and often the method of removing water from the mine, must have careful consideration. While a general discussion of the subject of hoisting is possible, most cases are entirely special, and can be considered only in connection with the peculiar conditions pertaining to that particular installation. The cost of installation of the hoisting-plant may be an appreciable amount, while the cost of raising the ore may be but a small part of the total operating-charge. In many cases, however, the output of the mine is limited by the capacity or the hoist, and the latter thus becomes of the first importance.

Jan 1, 1911

By J. F. Olk, E. D. Spaulding, R. E. Thurmond, G. A. Komadina, R. W. Hernlund, J. A. Journeay

THE Pima pit is a 1700x1400-St oval, the long T axis parallel to the strike of the orebody. The north side of the pit is carried as a final pit slope that coincides with the footwall of the orebody. The south side and east and west ends of the pit are working slopes continually being stripped back toward the final slopes. An inclined roadway extending from the natural ground surface on a 5 pct grade down to the north- east corner provides access to the pit. This road enters the pit 130 ft below the natural surface and continues as a pit ramp on a 5 pct grade to the 3150-ft bench (roughly the base of the alluvial cover). At this point the ramp system is steepened to a 12 pct grade and continues to the pit bottom. The 5 pct grade is maintained in the alluvial section to facilitate scraper haulage out of the pit. In addition to this main access ramp, temporary working ramps in the alluvial areas allow shorter routes to dumps. These are left on top of working benches and do not change the overall working slopes. Below the base of the alluvium, haulage is by truck down to the skip loading point or up from the bottom to the skip loading point.

Jan 4, 1958

By M. C. Leverett

KNOWLEDGE of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum pro-duction, but is as yet incompletely devel-oped. The object of this paper is to show the application of well established thermody-namic and physical principles to these prob-lems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: I. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion of mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. CAPILLARY EQUILIBRIUM IN SANDS Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treat-ment of problems of mixture flow, the con-cepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis-turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predict-able from the theory of capillary equi-librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, of course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is as-sumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reser-voir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems in-volving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately in-vestigated experimentally. Experimental evaluation of the pertinent properties of natural reservoir rocks will permit the ex-tension of the numerical treatment to prob-lems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids; that is, the manner in which the reservoir fluids are distributed vertically when the forces due to capillarity are just balanced by those due to gravitation.

Jan 1, 1940

By A. S. Adams

A GLANCE at the list of papers1 that have been published since 1920 on the general subject of flotation suggests the variety of ideas that exist regarding the underlying cause of the phenomenon. Among these ideas, we find several coherent theories, but none that adequately and completely explain the phenomenon. Ralston2 and Bains3 suggested an electrical theory which has to do with the attachment of mineral particles to a bubble by the attraction of unlike electrical charges. This theory has its root in the fact that a bubble of air in pure water is electrified in such a way that the surface is negatively charged while the body of the water is positively charged. This result, which was first discussed by Helmholtz, also obtains when the water contains anything except a high concentration of hydrogen ions, or ions which are trivalent or tetravalent. The theory also holds that the mineral particles have positive charges on their surfaces, and so there is attachment between bubble surface and mineral particles by the old law of electrostatics, which states that unlike charges attract.

Jan 1, 1928

Jan 1, 1951

By N. W. Sager, H. W. Mossman

The arrangement and general dimensions of the reverberatory furnaces and waste-heat boilers for the Nos. 2 and 3 smelting units at the McGill plant of the Nevada Consolidated Copper Corporation are shown in Fig. 1. Each of the two reverberatory furnaces has its own set of waste-heat boilers, and before February, 1932, each furnace, when it was in operation, delivered waste-heat gases to its own boilers only. In January, 1933, the idea was suggested of using some of the waste-heat boilers as economizers to operate in conjunction with the waste-heat boilers that were generating steam. The execution of this idea gave rise to the gas-flow scheme depicted in Fig. 1, the advantages of which were obvious, particularly so in view of the fact that for some months prior to the adoption of this scheme the smelting had been confined to No. 2 furnace, with No. 3 furnace and its boilers idle. The waste-heat gases from No. 2 furnace pass through the boilers serving this furnace as steam-generating units, thence through the original exit duct to a point where a bulkhead diverts the gases in a reverse direction through two of the boilers of No. 3 furnace. After the gases have traversed these two boilers, another bulkhead placed in the duct between No. 3 furnace and its boilers causes them to traverse still one more boiler, from which the gas path leads to the stack. In this scheme the last three boilers traversed by the gases, i.e., the boilers behind No. 3 furnace, function as economizers and preheat the feed water for the two steam-generating units directly serving No. 2 furnace. This discussion will give consideration to the results obtained in waste-heat recovery by the scheme shown in Fig. 1, and, further, will compare these results with those obtained before the boilers of No. 3 furnace were set up to act as economizers, but before going into the detail of heat generation, distribution and recovery, will present some additional details of the equipment. All boilers in this waste-heat plant are of the Stirling type. The two behind No. 2 furnace, acting as steam-generating units, of class 13, are 40 tubes wide and rated at 1112 boiler hp., while the three boilers behind No. 3 furnace, acting as economizers, are also of class 13, but 28 tubes

Jan 1, 1934

By K. Stout, L. Friel

Some rock mechanics theorists believe that if a hydraulically placed backfill can be introduced in a stoped out area, which will minimize wall closure by taking high stresses across the fill with minimum compaction, then heavy ground and rock burst phenomena will be minimized. The paper will discuss a large scale laboratory project when fill strength was increased over four times by the head vibrated method and up to well over 20 times by the double placed, cemented, vibrated head method when compared to conventionally placed fills. The only preconditioning of the 60% solids by weight slurry was the addition of cement in some tests.

Jan 1, 1983

By Reed S. C. Rogers, Robin P. Gardner, Kuruvilla Verghese

The development and use of short-lived radioactive tracer methods for the onstream determination of residence time distributions in large-scale ball mills is described. Tests are reported on a pilot-plant ball mill with 0.43 m diameter and 0.86 m length and on an industrial mill with 1.83 m diameter and 2.74 m length. Tests with different tracer feed sizes indicate that the residence time distributions on both mills are independent of charge particle size. Similar tests are planned for a large ball mill of 4.57 m diameter and 9.30 m length. No safety problems were encountered in these tests and none are anticipated in tests of the larger mill.

Jan 1, 1981

By Arthur B. Foote

Ore production from the property of the Miami Copper Co. began early in 1911. Until 1925 this ore came from the so-called high-grade orebodies, which contained a little over 2 per cent. copper. This ore was mined by the following methods: 1. Top slicing after mining the peaks by square setting, which produced 4,524,347 tons, including ore from square setting. 2. Shrinkage stoping with sublevel caving of the pillars, which produced 2,230,577 tons. 3. Undercut caving with hand tramming, which produced 15,427,672 tons. Estimating December tonnage, the total ore mined to the end of 1929 will amount to slightly more than 43,000,000 tons. The first method was described by E. G. Deane' and the second by D. B. Scott,' and the third, together with a general description of the mine, by J. H. Hensley, Jr.' The geology of the district has been worked out by Dr. F. L. Ransome.2 The author acknowledges also the assistance of R. W. Hughes, assistant mine superintendent, E. V. Graybeal, chief mine engineer, A. J. McDermid and S. R. Burdick, engineers of Miami Copper Co., Miami, Arizona. Factors Influencing Selection of Mining Methods The mining method described herein was selected primarily with a low mining cost in view and was developed to avoid as far as possible dilution of the already very low-grade ore. In 1924, with the exhaustion of the high-grade orebodies in sight, it was decided to develop the low-grade orebody, which at that time contained 36,000,000 tons of ore assaying 1.06 per cent. copper, and had an area of 50 acres with an average thickness of 206 ft. overlain by an average thickness of 320 ft. of barren capping.

Jan 1, 1930

By R. P. Corbett

Since the beginning of operations at the Kelley mine in 1952, Anaconda has emplaced more than 150,000 cu yd of concrete underground. Concreting practices have changed over the years but the net result is still the same- lower costs along the line and more versatility.

Jan 7, 1961

By Chandler Morse

RENEWABLE VS. NONRENEWABLE NATURAL RESOURCES Nonrenewable resources, such as minerals, are the inevitable center of attention in discussions of depletion and exhaustion. Nevertheless, it may well be proper to regard some nonrenewable resources as not subject to exhaustion, and renewable resources may sometimes be treated as if they were finite stocks. Thus, the availability of nonrenewable resources is not and probably never will be known completely Chap. 2.5A, and therefore is not subject to firm predictions concerning exhaustibility. Moreover, because exploration and discovery are more or less continuous processes it is often appropriate to regard mineral supplies as flows, and to treat the estimated reserves as working capital, an inventory, continually depleted by use and augmented by discoveries.23 The aggregate economically exploitable stocks of a given mineral are seldom estimated (or estimatable) with precision, as Chap. 2.5A shows, and even when they are, forecasts concerning years of remaining life can be and often are falsified by changes in one or more of the multidimensional conditions of supply and demand; or the productive services formerly derived from an exhausted stock may continue to provided without material impairment by one or more substitutes b Conversely, the renewable resources are all subject to depletion when the rate of use exceeds the natural or induced rate of replenishment, and cases of exhaustion or near exhaustion, as through soil erosion, overcuttmg of forest lands, and overfishing, are rather common c Where exhaustion is a clear possibility the resource may either be exploited on a consciously adopted "sustainable yield" basis or be treated as an exhausting asset." In some cases, conscious treatment

Jan 1, 1976

By R. R. Goddard

By use of the frequency response method with a radioactive tracer, it was possible to determine fluid dispersion and distribution in a natural consolidated and an unconsolidated medium. Measurements were made in a linear flow system at oleic saturations of 69 per cent in the consolidated medium, and 100 per cent in both media. Dispersion and distribution were obtained by measuring the amplitude attenuation and the phase velocity of sinusoidal waves with a dual monitor apparatus. The gamma ray emissions permitted in situ measurements at any distance along the porous samples. One result of importance was that the effective diffusivity increased as the wave length increased. As a consequence, a dispersion coefficient appropriate for the injection of large slugs might exceed the value measured by use of small slugs. Since flow models based solely on fluid velocity and an effective diffusivity coefficient imply that the diffusivity should be independent of frequency, such representations were not adequate for the data of this study. A comparison was made with a capacitance model of porous media with deadend PVs, but even this model was not completely adequate. By using attenuation and phase velocity data, fluid dispersion can be predicted without postulating a differential equation satisfied by the tracer concentration, thereby eliminating the need of a complicated model to represent dispersion. INTRODUCTION The flow of similar miscible fluids through a porous medium can be fairly adequately described by two parameters: the average fluid velocity and the effective diffusivity.1-3 It has been pointed out recently, however, that significant discrepancies exist between this representation and the experimental data.4-7 An improved agreement can be obtained by introducing additional parameters based on the concept of dead-end pores. The purpose of the present investigation was to find out whether the frequency response method could be used to measure the relevant parameters. The method was used in the following form. A stream of fluid was flowed at a constant rate through a sample of porous material and the concentration of a radioactive tracer in the fluid was varied sinusoidally at a fixed frequency. The effects of flow through a porous medium are a decrease in the amplitude of the concentration wave and an increase in the velocity of the peaks of the waves above the average velocity. Attenuation and phase veIocity of the waves were measured as a function of frequency and fluid velocity. The simple two-parameter model implies that the diffusivity should be independent of frequency. Data reported in this paper show that the diffusivity decreases as the frequency increases. Hence, as shown also by many others, the two-parameter model is not completely adequate. Coats and Smith 5 used two additional parameters in their model: the volume of the dead-end pores and the rate of mass transfer between dead-end pores and the flowing stream. Their capacitance model of a porous medium containing some stagnant fluid, to which transfer occurs by molecular diffusion, did not explain the dispersion results of either the present study or of theirs. Instead, the capacitance effect can be better described as the result of extreme velocity variations within the pores of the medium, with transfer between the velocity zones by convection. EXPERIMENTAL PREPARATION OF POROUS MEDIA Data reported here were obtained with a natural Berea sandstone, and with two packings of 20/25 mesh sand. Pertinent information about these media is listed in Table 1. The sandstone core was first sealed with a non-

Jan 1, 1967

By J. A. Herbst, R. Mackelprang, J. D. Miller

Droplet size distributions were determined by stabilizing in gelatin and measurement of the distributions by means of computerized image analysis Several variables that affect droplet sizes were studied and the resulting size distributions were modeled via a population balance equation Key parameters in the model were related to the physical properties and operating conditions of the systems examined using a multiple linear approach

Jan 1, 1981

By C. R. Ince

The term "differential flotation" is used to denote a flotation operation in which separation is effected between two or more minerals of the same class; e. g., lead sulfide from zinc sulfide, pyrite from blende, chalco-pyrite from pyrite, chalcopyrite from blende. At present, so far as published work shows, there seem to be two theories as to the mechanics of differential flotation. The earlier and more generally accepted theory is that the so-called depressing agents alter the surface of one or more of the sulfides in the ore, either by chemical action or adsorption, so that it is no longer amenable to flotation, but that these depressed sulfides can be revived, after the unaffected sulfide has been floated, by reagents which react chemically with the altered surface and make it amenable to flotation. More recently, Professor Taggartl has advanced the theory that slime adsorption is an important factor in differential flotation. He believes that, with the proper use of a class of agents, which he calls dispersion agents and which include practically all the depressing agents, one can cause the slime to adsorb differentially on sulfide surfaces. A gangue-slime coated sulfide surface will act as a gangue particle and will not float. If, subsequently, an agent that will remove the gangue-slime coating is added, the sulfide again assumes its original surface and can be floated as an ordinary sulfide. This is the basis of the slime theory of differential flotation. Timber Butte mill at Butte, Mont., is a typical lead-zinc flotation concentrator. Neihart ore, chosen for investigation in this work, is one of the custom ores treated at that mill. Practice at Timber Butte mill in February, 1928, was as follows: A combined lead-zinc concentrate was first made using 0.2 Ib. per ton on the ore of potassium xanthate and 0.03 lb. per ton of Cleveland Cliffs oil after 1.5 lb. per ton of lime and 1 lb. per ton of calcium chloride has been added just before the ball mill. The concentrate was then thickened to 70 per cent. solids. Potassium cyanide to the amount of 0.3 lb. per ton and zinc sulfate in the quantity of 0.5 Ib. per ton were added to the thickened pulp and the whole

Jan 1, 1930

By Leland Van Wert

IN 1888, Howard,1 working at the Watertown Arsenal on the tensile properties of ferrous materials at various temperatures, noted the curious fact that the stress-strain diagrams of low-carbon steels tested within a certain temperature range (200° to 350° C.) departed more or less from the normal regularity of such diagrams as secured by testing at either above or below these temperatures. This same jagged appearance of similar diagrams for steels has been observed by at least one other investigator, and de Forest2 has reported similar irregularities in the tensile testing of some nonferrous alloys. Recently again, this anomaly in diagram contour has been shown in a most striking fashion, apparently because of its accentuation by the method of testing employed, by Dr. Albert Sauveur.3 He described (for nonaustenitic steels) two quite distinct types of torsional stress-time diagrams: (1) those with a regular and smooth outline, derived normally by testing at temperatures above 300° C., or below 200° C. (as, for example, Figs. 4a or e); and (2) those presenting a decided "stepped" appearance, which are invariably produced when twisting is done within the 200° to 300° C. range (examples, Figs. 5a and b). The torsion test brings out so much more sharply (and convincingly) the irregularities occurring at 200° and 300° C. than does the tensile test that they can no longer be considered as resulting from simply idiosyncratic or accidental and inconsequential causes. Clearly, from the temperatures involved, the "stepped" type of diagram, or more accurately, the peculiar manner of response to torsional stress which manifests itself in the diagram, is an aspect of the "blue-heat" phenomenon. One's curiosity if, nothing else, prompts an inquiry as to the nature and significance of these "steps." What do they mean? What causes them? To these questions there are no completely satisfactory answers. The following experimental observations are offered as suggestions towards the solution of the problem.

Jan 1, 1931

By T. Koulomzine

The theory of the Askania mag-netometer, as well as a complete discussion of all factors influencing magnetometer readings, is very ably described by J. Wallace Joyce.1 We will assume that the reader is thoroughly familiar with this theory and we will use whenever possible the same notations for the physical values involved in the theory. On the other hand, we believe that the principal formulas of the magnetometer can be deduced much more easily by the use of differential calculus than by the methods employed by Joyce. Consequently, we are presenting herewith a resumé of the theory of the vertical magnetometer in order to determine the correct formula of the temperature coefficient which we propose to compensate. Short Theory of the Vertical Magnetometers We shall accept the following notations: m = total mass of the magnet system, in grams. g = acceleration of gravity, in dynes. a = projection on the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. h = projection on the perpendicular to the axis of the magnet system of the distance between the axis of support and the center of gravity of the magnet system, in centimeters. M = 2pL = M, magnetic moment of the magnet system. Z = vertical component of the earth's magnetic field. ? = deflection angle of the magnet system. = focal length of objective lens in the optical system S = scale reading. In a vertical magnetometer the axis of the magnet system is kept horizontal within 2". Therefore, referring to Fig 1, we see that the magnetic torque of the magnet system influenced by Z must be counterbalanced by the gravity torque. MZ cos ? = mga cos ? + mgh sin ? or dividing by cos ? MZ = mga + mgh tan ? If we now move to another magnetic station and the temperature conditions change, the values of all the variables will change also: M, a, and h under the influence of temperature. 2, both with time and space. ? and S, as a result of all the above changes. Taking increments in Eq 2 we obtain: (Mo + ?M)(Z + ?Z) = mgao + mg?a + mg(h + ?h) tan (? +??) but tan (? +??), because ? is small, can be replaced by tan ? + tan ??; in fact tan (?+ ??) = sin ?.cos ?? + cos ?.sin ??/ cos ?.cos ?? — sin ?sin ?? but sin ? sin ???0 tan (8 + ??) ? tan ? + tan ??. Fur-thermore, neglecting all terms of the equation containing two differentials becomes: or a differential and a tan ??, Eq 3

Jan 1, 1950

By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection' at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969