Search Documents

IN GATHERING material for this chapter on Yerington and the one to follow on Silver Bell, the A.S.& R. project near Tucson, Arizona, I was fascinated at the way the two stories paralleled each other. For example, here are a few instances: (1) The first copper mining in the Yerington district of Nevada was in the late 1860's; the first in the Silver Bell area in 1873. (2) Each district was served by a branch railroad about 25 miles long from a main line of the Southern Pacific (by quizzical coincidence); and, in each instance, the railroad was later abandoned and torn up. (3) Each district had a sizable blast-furnace smelter ten or fifteen miles from the principal mines, and in each instance the smelter was later dismantled for junk. (4) Up to 1954, the Yerington district was credited with a production of 100,000,000 lb of copper; the Silver Bell district with 80,000,000 lb. (5) In each district the entire production had come from deposits other than the low-grade ore bodies now being exploited. (6) In each instance, existence of the low-grade deposits of the Porphyry type was recognized in the period circa1910-1914 and a substantial amount of exploratory drilling had been done, on one deposit at Yerington and on two at Silver Bell. (7) In each instance, the properties containing the Porphyry ore were acquired by a strong company (Anaconda Copper Mining Company at Yerington and American Smelt-

Jan 1, 1957

By C. P. Gazzara and

The modulus of elasticity and yield strength of commercially pure, annealed titanium sheet was investigated at room temperature as a function of strain rate and direction of loading. The value of E varied with direction of measuremeni in the sheet but was unaffected by strain rate in the range 0.04 x 10-to 10-2min-1. The yield strength increased with increase it2 strain rate and varied with specimen orientation. VALUES of the modulus of elasticity, E, in tension for commercially pure titanium have been reported at from 14 to 20Xl06 psi.' Reasons suggested for this variation have been a) composition, b) strain rate, c) texturing, and d) creep. For example, alloys of titanium with aluminum, manganese, and nitrogen have yielded modulus values of from 12.5 to 16.8 x lo6 psi at room temperature.' It was shown by Klier that the modulus in titanium plate was sensi-tive to strain rate. while Dotson and kattus meas- ured variations in E as the strain rate was increased from 3X to 60 min-l. For RC-7OA, 0.040-in. titanium sheet at room temperature Dotson and Kattus found that the average values of E, for specimens in the rolling direction, increased from 14.7 to 16.0 X lo6 psi as the strain rate increased. Simultaneously, the 0.2 pct yield strength increased from 74,700 to 95,700 psi for the same specimens. Differences in yield strength and E have been reported as a function of directionality in titanium sheet.= Dotson and Kattus report such an effect, and Feola6 found in annealed titanium sheet marked anisotropy in tensile strength, yield strength, reduction in area and elongation at room temperature, with

Jan 1, 1961

By J. E. Burke

THE origin of so-called annealing or recrystalli-zation twins in face-centered-cubic metals continues to be a matter for speculation, and in the present report an attempt is made to explain their origin and to account for at least a majority of the observations concerning their behavior. The fact that annealing twins are prominent only The speelmen was deformed 8 pet in compression and then indented over the lower left-hand corner in a Rockwell in-denter, and then annealed to cause partial recrystallization. Note intense twinning in heavily deformed part and slight twinning in less deformed part. The upper right-hand corner is unrecrystalized. Area reduced approximately 25 pot for reproduction. after recrystallization suggests that deformation may be necessary for their formation. In 1926, Mathewson1 reported the observation by Phillips that annealing twins are frequently parallel to strain markings which delineate octahedral planes in the deformed (and partially recrystallized) matrix, and suggested that strain markings are mechanical twins which grow into annealing twins during recrystallization. Later work by Burke and Barrett' has shown that strain markings are traces of planes upon which slip has occurred, and that there is no evidence for the formation of mechanical twins of microscopically resolvable width in face-centered-cubic metals. Mathewson3 has pointed out, however, that slip may produce twin faults, and later modifications of this hypothesis have assumed that twin faults rather than true mechanical twins serve as the nuclei for annealing twins. Carpenter and Tamura5 suggested, also in 1926, that annealing twins might form by accidents of growth. A close-packed layer of atoms can be added to the octahedral plane of a face-centered-cubic metal in two possible positions, the right position

Jan 1, 1951

By R. A. Deju, R. B. Bhappu

The theory of electrophoresis is briefly outlined and an apparatus which may be used for electrophoretic studies is explained. The results obtained using this apparatus are in agreement with those obtained by other investigators. How to solve some of the complications which occur in the measurement of zero charge and zeta potential is explained. It is believed that the apparatus described in this paper will allow rapid measurements of zeta potential, zero point of charge, electrophoretic mobility and zeta coefficient. For many years the phenomenon of electrophoresis has been studied, and much work has been done in designing an apparatus for better measurements of mobility, zeta potential and zero charge of minerals. Up to the present, most electrophoresis experiments have involved cumbersome equipment and tedious microscopic observation. The modified cell proposed in this paper obviates these drawbacks by using a Rayoscope together with a special system of lenses and filters. It therefore allows a faster and more accurate measurement of zero charge and particle velocity. THEORY Most authors currently regard zeta potential as the potential difference in an otherwise uniform medium between a point some large distance from the surface of the mineral and a point on the plane of shear. Fuerstenau,1 Miaw,2 and Gaudin and sun3 have performed some calculations of zeta potential using Henry's equation.4 Their results show wide discrepancies, probably due to differences in the past histories of the minerals used. The authors have also noticed this difference on determining the zero point of charge of quartz as shown on Table I.

Jan 1, 1967

By William B. Heroy

LOOKING back over the industrial and commercial progress of the United States during the last half century the outstanding influence has been the growth of the use of the fluid fuels, petroleum and natural gas. At the turn of the century these fuels supplied only 8 per cent of the energy requirements of the nation. Last year nearly 45 per cent of our heat and power supply were derived from these fuels. These figures are merely statistical reflections of the fundamental change in our national economy which has affected, in so many amazing ways, the life of this generation. The factors which have caused this change are still operative. The trend which has thus been established still continues and growth in the use of these fuels is, in all probability, still well below the peak, both for this country and for other parts of the world. Two great wars have not essentially changed this basic trend; if anything they have served to accelerate it. World War II did not alone increase our requirements for liquid fuels; it demonstrated the absolute essentially of petroleum resources to our national security. Petroleum is no longer just an important factor in our national standard of living; it is the most important single element in our national defence-

Jan 1, 1946

John Birkinbine, Philadelphia, Pa.: We have in the Institute two Dudleys—Dr. Charles B. Dudley, who has so thoroughly studied the chemical composition and physical behavior of rail-steel, and Dr. P. H. Dudley, whose investigations and

Jan 1, 1900

By C. F. Quest, T. S. Washburn

The steel industry has a definite need in its tonnage mills for a formula relating expected tensile strength to the analysis of the steel. The McWilliam-Barnes1 and other less comprehensive formulas are used for this purpose, but these formulas were designed for an analysis range that does not include the medium manganese and silicon-bearing steels. This type of steel is being produced to meet the demand for tensile strength slightly higher than that of ordinary structural steel but not high enough to justify expensive alloy steels. The purpose of this paper is to present a somewhat more comprehensive formula based on data accumulated over a number of years by the Inland Steel Co., and to discuss the method followed in obtaining a formula to fit the data. The resultant formula admittedly is still weak in some respects, but for the expanded analysis range appears to be an improvement over the other formulas. It is hoped that with the collection of more data and possible collaboration with other mills studying this problem it will be possible to work out a more nearly perfect formula. Several publications have been issued on this subject. In some, the equation type of relation was evolved while others made a combination of tables and an equation. The latter include work by Campbel12,3 and Webster.4,5 Campbell classified the steels as acid and basic and applied a different formula to each. For basic steels, he used the equation: Teosile etrength = 41500 + 770C + 1000P + yMn [1 y was a variable depending on the carbon and manganese content of the steel and was listed in tables. Webster investigated acid Bessemer steel and developed the equation: Tensile strength = 38000 + 800C + xTP+ yMn [2]

Jan 1, 1940

By C. F. Quest, T. S. Washburn

The steel industry has a definite need in its tonnage mills for a formula relating expected tensile strength to the analysis of the steel. The McWilliam-Barnes1 and other less comprehensive formulas are used for this purpose, but these formulas were designed for an analysis range that does not include the medium manganese and silicon-bearing steels. This type of steel is being produced to meet the demand for tensile strength slightly higher than that of ordinary structural steel but not high enough to justify expensive alloy steels. The purpose of this paper is to present a somewhat more comprehensive formula based on data accumulated over a number of years by the Inland Steel Co., and to discuss the method followed in obtaining a formula to fit the data. The resultant formula admittedly is still weak in some respects, but for the expanded analysis range appears to be an improvement over the other formulas. It is hoped that with the collection of more data and possible collaboration with other mills studying this problem it will be possible to work out a more nearly perfect formula. Several publications have been issued on this subject. In some, the equation type of relation was evolved while others made a combination of tables and an equation. The latter include work by Campbel12,3 and Webster.4,5 Campbell classified the steels as acid and basic and applied a different formula to each. For basic steels, he used the equation: Teosile etrength = 41500 + 770C + 1000P + yMn [1 y was a variable depending on the carbon and manganese content of the steel and was listed in tables. Webster investigated acid Bessemer steel and developed the equation: Tensile strength = 38000 + 800C + xTP+ yMn [2]

Jan 1, 1940

By Toshihisa Adachi, Shosei Serata, Shunsuke Sakurai

Many different methods of measuring the in-situ stress field have been developed in recent years. They are all based on the assumption of elasticity without allowing any viscoelastic deformation. By using the high resolution strain-measuring technique recently developed in the laboratory at Serata Geomechanics, many rocks were found to be viscoelastic. The viscoelasticity of rock media was found to be dependent upon the resolution of the strain measurement. The higher the resolution of the strain measurement, the greater number of rocks could be identified as viscoelastic. All rocks eventually exhibit viscoelastic deformation under high stresses relative to the strength of the material. Therefore, the conventional methods of elasticity become less reliable with increase of ground stress. In deep underground formations, even hard rocks become viscoelastic. At the same time, many ground formations near the surface are actually viscoelastic. A new method was developed in the laboratory to determine the in-situ stress field in viscoelastic rock media. Rocks in general exhibit a small amount of viscoelastic creep whenever mean stress and octahedral shearing stress are changed substantially from their initial states. Such changes take place around a borehole immediately following the drilling although they are short-lived. We developed a viscoelastic method of determining the in-situ stress field by relating the time-dependent behavior of the borehole with the tensor properties and stress field of the underground. In developing the viscoelastic relation, only isotropic and homogeneous

Jan 1, 1970

By Bernard Moore

AT present the demands of the United States for strontium are met by imports from Germany, England and Canada, which vary considerably in proportions of ore and finished salts, in tonnage and in value. Statistics for the period 1926-1932 are given in Table 1. Domestic deposits are TABLE 1.-Strontium Imported into the United States, 1926-1932a Ore Chemicals Year Short Tons Value Pounds Value 1926 2,200 $58,159 5,433,044 $115,436 1927 1,356 58,711 4,233,816 149,383 1928 759 31,157 3,380,464 136,561 1929 973 45,505 4,578,327 196,233 1930 220 10,459 2,153,788 104.807 1931 (260 lbs.) 123 1,742,714 83,564 1932 5 276 469,481 20,910 a Mineral Industry (1934) 42, 61. known in many states, but the, larger and purer ones are in the West, particularly in the desert region of southeastern California and western Arizona. These deposits are large enough to command interest, par-ticularly in consideration of future cheap power at the Boulder Dam. The deposits described in this paper were examined during an investi-gation of the mineral resources of the Boulder Dam region by the United States Geological Survey for the United States Bureau of Reclamation in the spring of 1934. Mr. D. F. Hewett, who had general charge of the investigation, Mr. W. T. Schaller and Mr. M. I. Goldman contributed many helpful suggestions. Mr. N. H. Harshman assisted efficiently during the field work.

Jan 1, 1935

R. 8. MACPHERRAN, Milwaukee, Wis. (communication to the Secretary): The importance of carbon in pig-iron, as well as the desirability of buying, for some purposes, irons which are high in carbon, has always been recognized. Mr. Summers, I think, has given undue weight to the carbon-determinations. The combined carbon often decreases materially as the center of the pig is approached, with a corresponding increase in the graphite. Even the determination of total carbon, to be of service, must he supplemented by that of other elements. By it alone, the softness of a foundry-iron cannot be determined. Car-wheels and No. 5 iron, for instance, frequently contain 3.75 per cent. of carbon. This is the percentage specified by Mr. Summers for his No. 1 iron, " with the silicon about anywhere the furnace-man wants it." It is true that, other things being equal, the higher the carbon the softer the iron for foundry-use. But to introduce any given percentages of graphitic and total carbon into a pig-iron specification would but make the specification more complicated, without increasing its value in a commensurate degree. Mr. Summers does not believe in the governing of mixtures by the silicon, and, in support of his views, gives several tables. It seems to me that both his conclusions and his tables are somewhat unsatisfactory. He comments on the irregularity in carbon, but fails to note the significance of the irregularity in silicon..The variation of 0.7 per cent. in silicon, for example, is too great to be accounted for by difference in blast. It might better be attributed to bad grading at the furnace, unsystematic sampling, or irregular charging. Deductions drawn under such conditions are of little value. In ordinary work the castings from the same mixture should

Jan 1, 1899

By David R. Poirier

THE activity of carbon in Fe-C-Cr liquid solutions has been measured by Richardson and Dennis,1 Fuwa and chipman,2 and Goto et aL3 Fuwa and Chipman2 have presented their data along with data of Richardson and Dennis1 and utilized an interaction parameter. However, the interaction parameter is only valid for dilute solutions of carbon, because, as indicated, the same interaction parameter does not apply to more concentrated solutions of carbon (i.e., the effect of chromium on the saturation of graphite in liquid iron). Ohtani4 has attempted to account for the effect of carbon concentration on the interaction parameter; however even his analysis does not apply to the saturation data. Also, the effect of temperature on interaction parameters must be taken into account. Therefore, in any process where the concentration of carbon and/or the temperature changes (such as solidification), the use of an interaction parameter is not adequate to know the activity of carbon. The purpose of this communication is to make use of the existing data on the effect of chromium on the activity of carbon in liquid iron solutions in such a way that the activity can be described as a function of both composition and temperature. The method is an extension of Rist and chipman's5 analysis for the binary Fe-C solutions. As in Rist and Chipman's analysis, the activity coefficient is assumed to obey the relation: log y1 = at(l -X1)2 + It [1]

Jan 1, 1969

By F. Weinberg

WHEN impure Zn (< 99.99 pct)&apos;&apos;Z or Zn-Cd alloys3 are progressively solidified, a cell or "corrugation" substructure4 is produced in the solid, with a high impurity or solute concentration along the cell walls. When these materials are polished and suitably etched, etch pits are often observed along the cell walls. For the Zn-Cd alloys these etch pits have been associated with decorated dislocations, present in the corrugation boundaries to accommodate the lattice strain. In the course of an investigation of Zn-2 pct Au alloy, molten metal of this alloy was poured into cold water and the resultant solid pieces were sectioned, polished and etched with a Cr0 ethant. An extremely regular cell pattern was observed on the etched surface, similar in general to the corrugation structure previously reported for impure zinc and Zn-Cd alloys. At higher magnification, regularly spaced pits were observed along the cell boundaries. An example of the regular cell pattern at the center of a specimen is shown in the center and lower portions of Fig. 1; the top of the figure shows the pattern near the specimen surface. Typical etch pits in the cell walls are shown in Fig. 2. It was surprising that a cell pattern as regular as that shown in the center of Fig. 1 was produced at the very rapid solidification rates used (estimated as > 1 cm per sec). In addition, the distribution coefficient for the Zn-Au system is greater than 1. Accordingly, the center of the cells should be rich in solute and should etch

Jan 1, 1963

By R. L. Andelin, J. D. Knight, M. Kahn

Self-diffusion in single-crystal tungsten and diffusion of rhenium tracer in single-crystal tungsten have been measured over the temperature range 2660° to 3230°C by direct sectioning and radio-chemical analysis of W185 and Re183 and Re184 tracers. The initial radioactive layer was produced on the diffusion specimens by bombardment with 9.0-mev deuterons. Diffusion heating of the samples in high vacuum was accomplished by induction heating. Temperatures were measured by optical pyrometry, and the system was calibrated ALTHOUGH a considerable body of experimental information has been accumulated on self-diffusion in solids, the major part of the detailed work has by reference to the melting points of tantalum (2996°C), molybdenum (2620°C), niobium (2468°C), and rhodium (1966°C). The diffusion coefficients for the two systems, obtained by least-squares analyses of the data, are well-represented by the equations thus far dealt with relatively low-melting systems. Diffusion studies on the high-melting elements niobium,1 tantalum,2,3 and tungsten4&apos;5 have been limited to polycrystalline material, for which data interpretation and theoretical analysis are sometimes difficult. Only recently, a study has been made with single-crystal molybdenum.6 The present work deals with the measurement of self-diffusion in single-crystal tungsten at temperatures approaching the melting point (3410°c).7 Since the method chosen for producing the radioactive tracer layer-bombardment with deuterons—produced detectable isotopes of rhenium as well as of tungsten, the diffusion of rhenium was measured also.

Jan 1, 1965

By Frederick Laist

About six years ago the Anaconda Copper Mining Co. decided to investigate the possibility of extracting zinc from the ores of certain mines in the Butte district. These ores are of a complex character and contain so much iron and lead that the concentrate contains only 33 to 35 per cent. zinc. Investigations showed that while a high-grade concentrate could not be obtained by ordinary methods, such as tabling and magnetic treatment, a fair grade could be made by the Horwood process. In this method, the concentrate resulting from the flotation of all of the sulfides is given a light roast and this calcine is subjected to flotation in the presence of a large amount of sulfuric acid; the resulting concentrate contains most of the zinc and a residue contains most of the iron. The fact that the lead, copper, and silver are divided approximately equally between the zinc concentrate and the iron residue and the large consumption of acid, which ranged from 50 to 100 lb. (22 to 45 kg.) per ton of concentrates, were serious objections to this plan. The zinc recovery, moreover, was low, as a considerable percentage invariably accompanied the iron. While a profit might be made on the ores by the use of this process, it was thought that other and more promising methods might be devised. After carefully studying the field and doing some laboratory work on various processes that had been suggested, it was decided that the electrolysis of sulfate solutions was the most promising. We soon found, as have other investigators, that the only way to obtain a good zinc deposit is to have the electrolyte free from all metals more electronegative than zinc, such as copper, cadmium, lead, arsenic, antimony, etc. Arsenic and antimony are particularly injurious, causing very poor current efficiency and small yield per horsepower when present in amounts so small as almost to defy detection—1 mg. or less per liter. A pure zinc is soluble only with difficulty in sulfuric acid; an impure zinc dissolves very readily. Electrolytic zinc deposited from pure solutions is, of course, extremely pure and dissolves only about one-fiftieth

Jan 1, 1921

By Howard R. Hughes

In drilling for water and oil to reasonable depths through the generally soft yielding clay and sand formation of the Coastal Plain of Texas, Louisiana, and Mississippi, the rotating method of drilling was adopted, principally on account of the easy and quick penetration, and the low cost of the drilling plant. In favorable ground, free of heavy gravel and rock strata, as much as 1,600 ft. has been drilled in less than 36 hr., although such performances were of course rare. Hydraulic rotary drilling, or, as it is now called, rotary drilling, was used in the above States as early as 1880. The plant consisted of an ordinary derrick, a 25-h.p. boiler, a small hoist, a steam pump, and a water swivel with hose attachment, and an ordinary flat diamond-pointed bit. The successful drilling in of a phenomenal oil well by this process on Spindletop, near Beaumont, Texas, on Jan. 10, 1901, and the ascertained impracticability of drilling subsequent wells in the same locality by other methods (owing principally to heavy quicksand under pressure from below), brought rotary drilling into great prominence, practically to the exclusion of any other process throughout the Coastal Plain, and later on elsewhere. The method, as its name implies, involves the rotation of a pipe by means of machinery placed on the derrick floor. A drill bit attached to the lower end cuts a clearance for the drill pipe, with much the same motion and effect as an auger. Water forced through the drill pipe by means of a pump, and escaping through the bit, removes the cuttings and returns to the surface outside the drill pipe. In this manner the hole is kept open, permitting the drill stem to rotate freely. The pressure of the column of muddy water holds up the walls of the hole until it has been cased. Practically all the wells of the Gulf coast region, numbering nearly 10,000, have been drilled with this system. During the last five years its use has been extended to many other States and countries.

Jan 1, 1915

By A. L. Barnes

Residual oil in watered-out reservoirs is a tremendous reserve which has been unrecoverable by established production methods. A study of the new recovery methods indicated that the forward combustion urocess might- recover oil from such reservoirs; however, no thermal recovery operating experience in a watered-out system was available. The Delaware-Childers pilot thermal test was undertaken to test the feasibility of thermal recovery in this watered-out reservoir. The pilot test consisted of a 2.22-acre, inverted five-spot in the 600-ft deep Bartlesville sand. The reservoir in the pilot area had a porosity of 20.6 per cent, a permeability of 118 md and an average sand thickness of 45 ft. The reservoir contains a 33&apos; API, 6-cp oil. Combustion was started Nov. 22, 1960. The initial air injection capacity was 750 Mscf/D, but it was eventually increased to 2,000 Mscf/D. The test was surrounded by an active water flood; therefore, water production was initially high, but decreased as the heat wave moved toward the producing wells. Oil-bank arrival at an individual well was indicated by a drop in GOR and WOR, and an increase in oil production. Combustion-front arrival was evident at three of the pilot producers, and they were plugged. Cumulative oil production from pilot area wells war over 12,000 bbl. Operational difficulties were negligible and only conventional equipment was necessary. The combustion efficiency of this test averaged over 80 per cent. Results from coring showed that the leading edge of the combustion front tended to be wedge-shaped but a nearly complete sweep of the reservoir was eventually obtained. An isopach map based on evidence from 10 core holes and the existing wells showed that 126 acre-ft had been swept by the heat wave. Using this swept volume, an air requirement of 15.7 MMscf/acre-ft was calculated. It was calculated that 275 ,STB/acre-ft was consumed bv the heat wave. INTRODUCTION There is a large amount of oil remaining in reservoirs that have been water flooded. A study of ways to recover this oil showed that the forward combustion process might be applicable. Results from a number of forward combustion tests have been reported in the literature, but none of these tests were conducted in a watered-out system. The Delaware-Childers pilot thermal test was initiated in 1960 to define the operating characteristics of underground combustion in this watered-out Bartlesville sand reservoir, The purpose of this paper is to present the pilot test results in detail. FORWARD COMBUSTION PROCESS The forward combustion process consists of initiating combustion in the formation surrounding an injection well and driving this heat wave through the formation toward offset producing wells. As the combustion front progresses through the reservoir, oil and formation water are vaporized, driven forward in the gaseous phase, and recon-densed in the cooler part of the formation. These distilled liquids, water of combustion and gaseous combustion products, form a bank or three-phase region ahead of the burning front. This bank pushes mobile reservoir fluids toward the production wells. The rate of movement of the combustion front is controlled by the rate at which the nondistill able residue which serves as process fuel can be completely burned off the sand. The production performance from a heat wave conducted in a watered-out oil reservoir will differ from one conducted in a dissolved gas-depleted reservoir because of the difference in fluid saturations. The primary depleted reservoir contains connate water saturation, relatively high oil saturation and some gas saturation. The watered-out reservoir contains a highly mobile water saturation, residual oil saturation and little gas saturation. As the combustion front moves forward in either type of depleted reservoir, it drives the distillable oil, the water in place and the water of combustion ahead, and burns the nondistillable portion of the oil. The heat-wave process in a watered-out reservoir differs from the process in a

Jan 1, 1966

By RICHARD L. HUMPHREY

IT IS proper that there should be a brief accounting of the stewardship which was entrusted to the Joint Conference Committee by resolution adopted by the. Organizing Conference on June 4, 1920, in part as follows: RESOLVED, that it is the sense of this Organizing Conference that the Joint Conference Committee should be entrusted with making provision for putting the conclusions of this Conference of engineers into effect, etc. Pursuant to this authority, the Joint Conference, Committee has acted as an Ad-interim Committee has- prepared, a synopsis of the proceedings of the Organizing .Conference, has edited and published the Constitution and By-Laws adopted by this Conference, and. has issued an invitation to become Charter Members of The Federated, American Engineering Societies; to the list of organizations to whom invitations had been extended to attend &apos;the Organizing., Conference. The Committee in connection with this invitation offered to the extent of its ability, such assistance as might be-desired; and arranged in many cases for one or more of its members to be present when the matter of membership in The Federated American Engineering Societies was considered. . .

Jan 1, 1920

By H. Souder

The object of this paper is to bring to the notice of engineers a safety detonating fuse by the use of which misfires in blasting may be eliminated and safety in blasting operations promoted.

Jan 1, 1915

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958