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By Hugh H. Waesche

High quality quartz crystals weighing more than 50 grams are required in several important industrial applications.30,31 Primarily, they are the basic raw material for precision, electronic, frequency control components; this includes oscillators and filters in both radio and telephone services. Quartz crystals are also necessary for optical lenses and prisms in special applications requiring high ultraviolet light-transmission as in spectrographs. Quartz wedges are regular components for petrographic microscopes. The application of crystalline quartz as a transducer* in ultrasonic devices has increased in recent years despite strong competition from barium titanate and magnetostrictive [f] devices. Some quartz is fabricated into delay lines for radar. Man has valued quartz for fabrication of art objects since the dawn of history. The art forms were and are painstakingly carved and polished to form intricate figurines, bowls, statuettes, and the well-known crystal balls. The largest known ball, made of perfect quartz from Burma, is now in the National Museum in Washington. It is 12 7/8 in. in diameter and weighs 106 lb 12 oz. Clear, pure quartz chips and small crystals not meeting the electronic-grade dimensional requirements are known by the Brazilian term lasca. They are used to produce fused quartz having wide application in laboratory equipment, as special glasses, for torsion suspension in scientific instruments, and as a source material for growing large artificial quartz crystals 18,35 Electronic applications far exceed all other uses in importance so any discussion of high-quality quartz crystals must be concerned almost exclusively with those functions. Historical Background Because of their ubiquitous character and natural beauty, quartz crystals have long been of interest and known to man. They have been found among early Egyptian and Chinese art forms and the Sumerians are believed to have fashioned seals, beads, and other jewelry from quartz crystals, perhaps 5,000 years ago. Also, American Indians made arrow heads and fashioned some simple objects of different kinds. The origin of the name quartz, although of Greek derivation, is uncertain. The Greeks appropriately applied their word for frozen water or ice, krustallos, to quartz. The present-day, large-scale practical applications of quartz crystals began in 1880-1881 when Pierre and Jacques Curie reported discovery of the "piezoelectric" effect. They found this effect first in Rochelle salt, a common product of grape-wine refineries, while studying crystal symmetry. Piezoelectricity is that property found in certain crystals, including quartz, whereby electrical charges of equal and opposite sign appear on opposite parts of the crystals when they are stressed. If equal and opposite forces are applied to two opposing prism edges of a single untwinned quartz crystal a positive electrical charge will appear on one edge and a negative charge on the other. The amount of the charges will be directly proportional to the force applied. This property seems to be intimately related to pyroelectricity

Jan 1, 1960

By Ernest R. Darby

If the correct balance between fuel and air is maintained in an open-flame furnace,' little chemical action may be expected between the products of combustion and the metal being melted. Physical' changes in the metal are the object of the melting operation, and indirectly, under certain conditions, may be the cause of subsequent chemical actions. If sufficient heat has been introduced into the metal to bring about the change from the solid phase to the liquid phase, and still further from the liquid to the vapor phase, the metal vapor in all probability will be carried from the furnace by the exhaust and rapidly combined with the oxygen of the outside air. The charge being melted in the furnace may contain elements which are chemically inactive at normal temperatures but which will form compounds at the elevated temperatures of the metal bath, or even at a lower degree. Such indirect chemical actions are very confusing and often lead to incorrect conclusions regarding furnace atmospheres. In the open-flame furnaces used in the melting of bronze, the furnace atmosphere is spoken of as being either neutral, oxidizing or reducing in its effect upon the metal. A neutral atmosphere, as mentioned, is generally considered as the atmosphere of the furnace that will produce melted bronze, neither oxidized nor gassed. It is in effect an atmosphere which is not directly the cause of any chemical action. In such an atmosphere absolutely pure metals may be melted and poured without the absorption of gases or the formation of metallic oxide. The metal has undergone a simple, physical change. An oxidizing atmosphere is one in which the air introduced to the furnace is in excess of that required to complete combustion of the fuel used. The oxygen of the excess air may combine with the metal being melted to form metallic oxide, which may or may not be dissolved by the metal. If an absolutely pure metal is melted in a furnace operating with such an atmosphere, a portion of the metal charged may be converted into metallic oxide, the amount depending upon the duration of the

Jan 1, 1930

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates are required for certain end uses, and these are produced from smaller colemanite-ulexite-probertite bodies. Sodium-free borate compounds also are produced from boric acid, which can be manufactured from either sodium or nonsodium borate minerals. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of over a million tons of B2O3. Leadership in supplying borates shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates, In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, CA is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, CA, the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "10-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7 • 10H2O. In addition to ship¬ping all major refined borate products from [ ]

Jan 1, 1983

By A. R. Powell

Four, general methods have been used in the study of the decomposition of coal. The first has been directed toward the processes of coal formation, the second has been by means of microscopic studies, the third from the data of destructive distillation, and the fourth has made use of various solvents. Applying these methods to the sulfur of coal, it has been found that the organic sulfur of plant and animal life enters into the formation of coal and remains in organic combination in the final product. The inorganic sulfur is almost entirely combined as iron pyrites and marcasite. The infiltration of hydrogen-sulfide waters is doubtless a large factor in these combinations. Sulfates are found in very small quantities except where free oxygen has entered the coal strata. The mechanical mixing of detritus with the early coal material is another source of sulfur. In this case the sulfur is distributed in microscopic particles throughout the mass. In destructive distillation, a part off the sulfur comes off as hydrogen sulfide and various thiophen compounds, but this furnishes little information as to the nature of the sulfur compounds in the coal itself. The use of solvents has given valuable data concerning the sulfur compounds in coal. Fremy1 and later E. Guignet2 noted the action of alkaline solutions on coal after treatment with nitric acid and Anderson and Roberts3 showed' the presence of large quantities of organic' sulfur in the extract so obtained. In a study of the phenol extract of coal, Parr and Hadley4 found organic sulfur in the soluble organic material. These investigations proved the presence of organic sulfur in coal in addition to the inorganic forms, such as iron pyrites and sulfates. T. M. Drown5

Jan 9, 1919

By Thomas Watson

Introduction THE occurrence of zircon in pegmatites of acidic composition is recorded by many observers both in this country and abroad, and they form one of the most important geologic modes of occurrence of the mineral.' As is well known, commercially the most important American locality for zircon is near Zirconia in Henderson County, North Carolina, where many tons of the mineral have been obtained from a kaolinized pegmatite dike 100 ft. wide and traced for 1 ½ miles along the direction of strike N. 50° E. Zircon may be developed in pegmatites as inclusions in the principal rock-forming minerals, chiefly quartz and feldspar, and as a separate megascopic constituent in the form of grains and crystals not exceeding, as a rule, 2 in. in size, and usually smaller. In the Henderson County, North Carolina, pegmatite, zircon occurs in prismatic crystals with pyramidal terminations measuring up to 30 mm. in diameter, associated chiefly with the feldspar. In some of the apatite veins of Canada, which are closely allied to pegmatite dikes, zircon is reported in crystals upward of 6 in. in length and 2 in. 'and more in thickness. Zircon in large masses occurs in Virginia in the well-known pegmatites near Amelia in Amelia County, and near Gouldin in Hanover County. Both localities are in the middle eastern portion of the Piedmont Plateau province, and are separated by a distance of about 40 miles in a northeast-southwest direction. The rocks of both areas, including the pegmatite bodies, are in an advanced stage of decay, and, the hard and moderately fresh rocks are concealed beneath a cover of variable thickness of rock decay derived by the normal processes of weathering. Exposures, there-

Jan 7, 1916

By E. P. Abrahamson, S. L. Lopata

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deforlnation gradient matrix, F - [axi/aXj/ where X and x refer lo the initial and final positions of a particle. This matrix is readily evaluated in termas of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip systena. In the case of deforma tion from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Göler and Sachs.4 Taylor and Elam1 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, ! terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(aN as N — m while a — 0 in such a way that the Product Na = a finite conslant designatzng the accumulated amount of shear. It turns out that this limit is simply eafF1, where F, is the matrix whose elements are the coefficients of a in the F(a) twatrzx. Application is made of the present treatment to a fcc crystal of Permalloy compressed on the (110) plane and contrained to elongate in the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to (xl,xz,x3), both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By E. S. Leaver

THE amount of gold that occurs in a ton of milling ore from most of the large-scale copper mines is so small that unusual care and special attention are necessary to recover it. In some cases the gold is not considered important enough to warrant daily assays of the various products. Considering the large tonnage of copper ores that are now concentrated by flotation, as computed in a recent review, the gross gold content is surprisingly large, probably amounting to over 10 million dollars per year in the United States. The indications are that in many of the copper-milling operations with gold content under $1 per ton, only 50 per cent. of the gold is recovered in the flotation concentrates. Lime is generally used as a depressant for pyrite in the flotation circuit. The authors have shown that high lime or a solution high in calcium ions is also a depressant for gold. Their experiments on several well-known ores show that by careful regulation of the alkalinity of the mill solutions, a higher flotation recovery of the gold can be obtained, together with equally good copper recovery in a good grade of copper concentrates. In cyanidation for the recovery of gold, the best accepted practice demands that the mill solutions be tested and regulated by simple chemical reactions at definite periods during treatment or with each change in the treatment. It is similarly important for the recovery of gold that the solution in the flotation circuit be analyzed for calcium ions at regular periods and at each step in the flotation practice. The lime should be added when and where needed and not in excessive amounts at the head of the mill.

Jan 1, 1931

By John L. Lamont, Walter Crafts

ADEQUATE hardenability has long been recognized as one of the first requirements for producing desired mechanical properties in a heat-treated steel. Since the introduction of the Jominy end-quench test1 and the development of correlative information to expand its use, industry has had an effective measure of hardenability. Prediction and control of the hardenability have been made possible by Grossmann's principle2 for calculating hardenability from chemical composition; and Field's conversion3 from depth of half-martensite hardening to Rockwell C hardness has made the relation more quantitative. These developments have facilitated the design of new steels and the control of standard grades to the extent that it has been possible to establish tentative hardenability bands for some of the more commonly used alloy steels.4 As the depth of hardening of the Jominy test specimen is usually measured by Rockwell C hardness, it was considered that it should be possible to predict the hardness by a more direct calculation. It has been found that this can be accomplished by the addition of Rockwell C units proportional to the carbon and alloy content, grain size, and position in the Jominy test specimen. The calculation has been found to be fairly accurate, and because of its additive character is relatively simple to use. In principle the method of calculation is somewhat similar to the expressions developed by Herty, McBride, and Hollenback,5 Burns, Moore, and Archer,6 and Burns and Riegel.7 The calculation is started from a base that includes the effects of carbon content and position in the Jominy test speimen. Rockwell C units are added to the base in proportion to the alloy content and grain size. This sum represents the Rockwell C hardness up to the level at which a disproportionate increase of hardness is caused by the formation of martensite, and above this level an increment for martensite hardening is added. The effects of alloys are directly proportional to the amounts present and are independent of each other, the carbon content, and the position in the specimen. Furthermore, the factors for determining the martensite increment are dependent only on carbon content and are independent of cooling rate and alloy content. It is this absence of interrelation between the different factors that makes it possible to calculate the hardness and makes the method of calculation consistent with the principle that the character of the hardening reaction is governed primarily by carbon and that alloys exert their effect chiefly through control of the critical cooling rate. The principle of the calculation, and the effects of alloys on the critical cooling rate,

Jan 1, 1945

By J. G. Koenigsberger

The electrical specific resistance of rocks in the field is measured by sending a current through a medium of great volume, compared to the electrodes, whose resistivity should be measured. The whole resistance can be determined by the Wheatstone bridge and the specific resistance calculated by a well-known formula. The resistivity of some rocks in place in Germany and in Switzerland is given; first, of a rock near the surface, and especially near electrodes. Practical applications are made in the determination: (1) of the continuity of a conducting orebody; (2) of the surface ares of an orebody; (3) in the detection of a water-bearing fault in a salt mine. Preliminary 'observations are described: (1) on the influence of the depth of ground-water table; (2) on the detection of gas under high pressure in coal seams. The observations in this paper of the electrical resistivity of rocks and soil in place are along the lines of the very interesting method and results of the Messrs. Gish, Rooney, Hotchkiss and Fisher. 1,2 All the work described has been done since 1920. Method Used The very simple method consists in the application to the rock of two plane circular electrodes of iron or brass of a suitable diameter, with the aid of a contact substance, and in measuring the resistivity in a Wheatstone bridge with alternating current of 100 to 400 Hertz frequency per sec.). The general formula is known to be R= R0 +d/4(1/a+1/b-1.7/l+0.8(a+b)/l2) (1)

Jan 1, 1929

By W. A. Krivsky, R. Schuhmann

PREVIOUS papers in this series on the thermo-•t dynamics of copper-smelting systems have presented a survey of the field and an outline of the overall program: thermodynamic studies of iron silicate slags, 2-4 and thermodynamic data for simple mattes in the Cu-S system.5 Since this program was started, an excellent summary of the whole field of physical chemistry of copper smelting was published by Ruddle. The present paper represents a further step in the study of liquid mattes, and deals specifically with the Cu-Fe-S system. The importance of the Cu-Fe-S system to copper smelting is evident from the fact that these three elements constitute 90 to 99 pct of the totalweight of most commercial mattes. In copper mattes oxygen is an important fourth component. Oxygen was rigorously excluded in the work to be described in this paper. However, the behavior of oxygen in mattes was the subject of a companion research by Lander' which will be described in a subsequent publication. Several studies have been made previously of phase equilibria in the Cu-Fe-S system,8-10 so that the ternary phase diagram is fairly well established in most regions. Also, separate studies have been made of the phase diagrams and thermodynamic properties for the three binary systems: CU-S,5,12-15 CU-Fe,11,14,17 and FeS.11,14,16,17 However, no work has

Jan 1, 1958

By T. E. Kihlgren

SYSTEMATIC data are presented on the relation of composition of nickel silvers to color, tarnish resistance, hardness and liquidus temperatures, for alloys containing up to 30 per cent nickel and 50 per cent zinc, further modified at certain nickel and zinc contents by 0 to 8 per cent of tin and 0 to 10 per cent of lead. Attention has also been directed, using a still more limited range of alloys, toward a study of tensile properties and such casting properties and characteristics as fluidity, shrinkage and pressure tightness. In some of these, rather broad ranges of composition are dealt with; in others, it has been expedient to focus attention on the Federal Specification 20 per cent nickel silver casting alloy, WWP-541. INTRODUCTION The demand for an alloy essentially white in color, which could be cast and worked by simple methods and which possessed strength and corrosion-resisting properties superior to the usual brasses, led to the discovery and early use of cupronickel alloys containing zinc, and some-times tin, lead and other metals. This type of alloy was generally known as German silver until the war, when the term "Nickel Silver" became generally accepted. The element principally responsible for the white color of the alloy and for its strength and corrosion resistance is nickel, which may constitute from 8 to 30 per cent of the alloy. The functions of the other elements will be described later. The manifold uses of nickel silver are largely due to its color, corrosion resistance, ease of casting, fabrication, joining and rather moderate cost. In many instances the alloy is finished by grinding and polishing while in others it may be finished with a silver or nickel plus chromium plate. Electroplates

Jan 1, 1935

By Thomas L. Watson

The occurrence of zircon in pegmatites of acidic composition is recorded by many observers both in this country and abroad, and they form one of the most important geologic modes of occurrence of the minera1. As is well known, commercially the most important American locality for zircon is near Zirconia in Henderson County, North Carolina, where many tons of the mineral have been obtained from a kaolinized pegmatite dike 100 ft. wide and traced for 1 1/2 miles along the direction of strike N. 50" E. Zircon may be developed in pegmatites as inclusions in the principal rock-forming minerals, chiefly quartz and feldspar, and as a separate megascopic constituent in the form of grains and crystals not exceeding, as a rule, 2 in. in size, and usually smaller. In the Henderson County, North Carolina, pegmatite, zircon occurs in prismatic crystals with pyramidal terminations measuring up to 30 mm. in diameter, associated chiefly with the feldspar. In some of the apatite veins of Canada, which are closely allied to pogmatite dikes, zircon is reported in crystals upward of 6 in. in length and 2 in. and more in thickness. Zircon in large masses occurs in Virginia in the well-known pegmatites near Amelia in Amelia County, and near Gouldin in Hanover County. Both localities are in the middle eastern portion of the Piedmont Plateau province, and are separated by a distance of about 40 miles in a northeast-southwest direction. The rocks of both areas, including the pegmatite bodies, are in an advanced stage of decay, and the hard and moderately fresh rocks are concealed beneath a cover of variable thickness of rock decay derived by the normal processes of weathering. Exposures, there-

Jan 1, 1917

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By Henry A. Stiff

The classification and correlation of water analysis data presents many problems which can be solved by graphic methocis. The pattern system, a new type of graphic procedure described in this communication, is believed to have several advantages over older methods. Examples of the application, of the pattern system to the solution of problems encountered in petroleum production are given. INTRODUCTION Several graphic methods for presenting analytical water data have been developed and are now in use.1,2,3,4 It is believed, however, that a recently developed type of graph called the "pattern" offers several advantages over other methods. This system presents a better picture of the total salt concentration than is usual in such graphs. The effect of dilution or concentration has been reduced to a minimum, and at the same time distinction between various types of water has been improved. The system is extremely versatile, yet so simple it can be plotted on ordinary graph paper and adapted to almost any type of filing system. DISCUSSION The essential feature of the pattern system is the graph shown in Fig. 1. Horizontal lines extending right and left from a vertical line at zero form the graph. Positive ions are plotted to the left while negative ions are plotted to the right. The figure immediately beneath each ion gives the scale. Most oil field waters can be plotted on a scale where 100 milli-equivalents of sodium and chloride and 10 milliequivalents of each of the other ions are represented by one scale unit. For highly concentrated brines, 1,000 milliequivalents of sodium and chloride and 100 milliequivalents of each of the

Jan 1, 1951

By Edward Wichers

THE purpose of this paper is to set forth the matters of principal interest in connection with work done in the past few years on the purification of the metals of the platinum group, including the study and modification of methods already in the literature and the development of new procedures. For the most part, the results will be given in summary form, reserving the publication of detailed data and directions for a forthcoming paper to be issued by the Bureau of Standards. In recent years increasing interest has been shown in the preparation of the pure platinum metals, both by those concerned with the manufacture of the metals and their alloys for scientific and industrial purposes and those who are engaged in the study of the chemical or physical properties of the elements. The purification of the metals usually has been regarded as a matter so involved and difficult as to require the attention of specialists. It is hoped that this paper will show that any of the metals can be prepared in any desired degree of purity by relatively simple straightforward chemical methods. For the most part, it is thought that the methods given are suitable for small-scale refineries as well as for the laboratory; also, that they will bring the time required for the purification of any of the metals within reasonable limits. The new procedure suggested for purifying platinum should prove to be much shorter than any methods described in the literature.

Jan 1, 1928

By C. R. Johnson, R. A. Greenkorn, G. W. Widner

This paper describes a short, simple well-testing procedure evolved from unsteady-state concepts to appraise wellbore damage in water-input wells. Input rates are changed at specific intervals over a 30-minute period and the wellhead pressure recorded at the end of each interval. From these data, the pressure drop due to the "skin" can be computed. This pressure drop in terms of psi/B/D of input rate is referred to as the "skin factor". Two of these variable-rate tests are required to determine change of wellbore damage and to evaluate well-treatment techniques. There are several advantages to the variable-rate procedure. The necessary data can be obtained with wellhead gauges and meters. There is little interference with normal operations. The short testing period eliminates many interpretative difficulties that come from interference from adjacent wells. The shut-in period required for standard tests before the plot of pressure vs log of time attains a straight line is often 12 hours or more. Such a time period is incronvenient, especially when a well must be tested repeatedly to evaluate change in wellbore characteristics. This variable-rate procedure has been successfully npplied to water-input wells in three fields. For some of the wells, skin factors were calculated from both the standard and the variable-rate tests. These results show good agreement. THEORY OF THE VARIABLE-RATE PROCEDURE In many waterflood input wells, the pressure in the wellbore differs from the pressure in the reservoir immediately adjacent to the well because of the restriction of flow through the skin of the well. If the true pressure of the reservoir at the well, p,, is that pressure which would exist in the well if no skin were present, and p,' is the actual pressure as measured in the well, this difference, is the skin effect. Fig. 1 shows the change in skin effect with change in flow rate. As the flow is reduced, the skin effect is reduced by an amount equal to the change in wellbore pressure minus the change in reservoir pressure. The equation of pressure change without skin using the point-source solution of the diffusivity equation is (after van Everdingen')

By Edward Saibel

THE various theories that have been advanced to explain or predict the conditions under which a metal fractures may be divided into two categories: First, there are the macroscopic theories generally used in engineering practice. These are empirical in nature and limited in application. For example, the maximum normal stress criterion, which is quite satisfactory for a mild steel in simple tension at atmospheric pressure, no longer suffices when this steel is pulled under hydrostatic pressure.2 In all of these empirical theories, the critical condition characteristic of the material and of the loading conditions must be obtained experimentally. Secondly, there are the theories based on interatomic forces,3,4 or on the energy required to form new surface.5,6 These have all dealt with the theoretical evaluation of the tensile stress necessary to bring about rupture in a purely brittle manner; that is, without plastic flow preceding fracture. All of these attempts have led to values of the tensile strength of crystals or of polycrystalline bodies that are 100 to 1000 times higher than observed values. On this account, it has been thought necessary by some investigators to conceive of a microcrack structure or distribution of flaws throughout the specimen such that the resulting stress concentrations provide the factor necessary to bring about agreement between calculation and experiment. It has been pointed out by several observers7 that this point of view is highly unrealistic, in that the weakening effect of these flaws or microstructures must be very uniform from specimen to specimen, since the fracture stresses found for various specimens of the same material tested under similar conditions are so - nearly constant. Furthermore, since calculations based on atomic forces or atomic energy are for purely brittle fracture, a condition probably never satisfied in tests, agreement is hardly to be expected. Thermodynamic Theory Of Fürth In order to resolve this apparent discrepancy between the theoretical cohesive strengths and the observed fracture strengths, Fürth8 advanced a thermo- dynamic theory of the tensile strength of isotropic bodies based on work of Born9 relating to the melting of crystals. Assuming an isotropic material free from imperfections and flaws, behaving elastically up to the breaking point, and assuming a connection between rupture and the melt- ing phenomenon, Fürth obtains an expression for the rupture stress u, in the form [ ] where Q is the melting energy per unit mass, ? is the density, and µ is Poissons’ ratio. Fürth compares fracture stresses computed from Eq I with the fracture stresses of metals as given in the Landolt-Bernstein Tables (1927) and in the Hand-

Jan 1, 1947

By W. B. Lilienthal, J. C. Melrose

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By J. C. Melrose, W. B. Lilienthal

The application of Bingham's law to the behavior of drilling fluids in a rotational viscometer permits the expression of viscometric data in terms of plastic viscosity and yield value, the flow properties of a plastic fluid. A commercially available rotational viscometer is described, and when modified to a multispeed type viscometer, is shown to provide a simple and convenient instrument for the measurement of these properties both in the laboratory and in the field. The data obtained are shown to be useful in defining and understanding mud control problems relating to chemical treatment and to the hydro-dynamic behavior of muds. INTRODUCTION The highly complex drilling fluids which are required for deep drilling often give rise to new and unusual mud control problems. Rapid and economic solutions to these problems may require, on the one hand, better understanding of the changes which contaminants and chemical treating agents produce in the colloidal and inert solids of the mud, or, on the other hand, closer control of the hydrodynamic behavior of the mud. The latter objective obviously can be achieved only if a correct rheological analysis of the flow behavior of drilling muds is available and if this is accompanied by the appropriate rheological measurements. The purpose of this paper is to describe such measurements in the field, and to show how the resulting data can be of value in solving difficult mud control problems. It is now generally recognized that Bingham's law of plastic flow can be utilized in describing the hydrodynamic behavior of drilling fluids in the non-turbulent flow range. Beck, Nuss, and Dunn' have recently applied this law to the flow of mud in small pipes, and Rogers2 has reviewed the rather extensive literature on this subject. So far, however, the use of Bingham's law has been restricted to the analysis of mud flow in pipes or capillary tubes, and it has not been directly applied to the flow in rotational viscometers. In the work to be reprted, the Reiner-Riwlin3 equation for the flow of a plastic fluid in a rotational viscometer has been utilized to permit the expression of multispeed viscometric data in terms of plastic viscosity and yield value. the two absolute flow properties of a plastic fluid. With regard to the application of these measurements, the calculation of the relationship between pumping rate and pressure drop, both in the drill pipe and annular space, has long been a subject of interest. Beck, Nuss, and Dunn,' following Caldwell and Babbitt: base their calculations for non-turbulent flow on Buckingham's integration of Bingham's law for pipe flow and measurements of the plastic viscosity (rigidity in their terminology) and yield value. In the case of turbulent flow, Fanning's equation is employed, and the pressure drop is relatively insensitive to the flow properties of the mud. Since flow in the drill pipe is likely to be turbulent at usual circulation rates, the plastic flow properties will chiefly influence the pressure drop in the annular space. As pointed out by Beck,' the control of this component of the total pressure drop may be of special importance where lost circulation problems are encountered. Other hydrodynamic problems to which it should be possible to apply measurements of the plastic flow properties include predictions of the velocity distribution in non-turbulent flow and the critical velocity for transition to turbulence. Plastic viscosity and yield value. as abmlute flow propertie.;, will reflect the colloidal or surface-active behavior of the solids present in drilling fluids. Measurements of these properties should therefore find application in developing a better understanding of such behavior and in characterizing the type and condition of these solids. Garrison and ten Brink have utilized multispeed viscometric data in this manner. although their measurements were not expressed in terms of the absolute flow properties. In connection with the application of these measurements, it should be recognized that the presently used one-point viscosity measurements are relative in nature. The API Stormer 600-rpm measurement, for example. is a function of both plastic viscosity and yield value, as well as mud weight, and will often be misleading when its application to mud control problems is attempted. NOMENCLATURE, UNITS, AND DEFINITIONS In Fig. 1 an idealized plot is given of the flow variables involved in any viscometric measurement. It is seen that the flow behavior of plastic fluids is characterized by two constants — plastic viscosity, µp, and yield value, F. Other workers hate used the term rigidity for plastic viscosity or the term mobility for its reciprocal. The term plastic viscosity, however, emphasizes the close relation this property bears to the viscosity of a true fluid and is expressed in the familiar viscosity units of centipoises. The yield value is expressed in lbs/100 sq ft, the units adopted for gel strength measurements with the APT shearometer. Definitions of these properties based on rheological or macrc)scopic flow considerations follow from Fig. 1. The plastic viscosity of a substance obeying Bingham's equation is defined

Jan 1, 1951

By Donald W. Scott

GENERALLY speaking, there is nothing very difficult about taking good micrographs of photogenic thin sections or grains with a petrographic micro-scopecamera setup. However, sometimes it is desired to show some detail that cannot be illustrated satisfactorily by the usual micrographs taken with parallel polarized light, with crossed nicols, or even with two micrographs. A simple procedure giving good results has been used at Battelle Memorial Institute for subjects falling into this classification, and it is believed to be of interest, especially to research people who must sell a point to executives through the medium of well-illustrated reports. The following problem illustrates a typical application: It is desired to photograph a thin section of an iron ore to illustrate the character and association of the iron oxides and the individual quartz crystals. A magnification of 75 dia. is acceptable. A micrograph of the field in question (Fig. I[a]) was taken with parallel polarized light. Due precaution was taken to provide critical illumination, correct exposure, a sharp focus, a good darkroom technique, and other essential conditions. It illustrates correctly the iron oxides, but it fails to show the individual quartz crystals. A micrograph of the identical field (Fig. I[b]) was taken under the same precise conditions, but with crossed nicols. It gives a better idea of the character of the individual quartz crystals but is likely to be misinterpreted unless accompanied by a lengthy descriptive note. This micrograph suggests that the centrally located, large black area is composed entirely of iron oxides. That this is an incorrect interpretation is evident by reexamining the micrograph of Fig. I[a]. The correct interpretation is that the dark area contains quartz crystals oriented with their optical directions parallel to, or nearly parallel to, the vibration directions of the polarizer and analyzer of the microscope. Thus, the executive, or anyone who had not done the work personally, would get no more than a fair interpretation, even if two micrographs were included; and in the interests of both brevity and clarity, one micrograph usually is more desirable. Exactly how many quartz crystals occur in this region cannot be told from the two micrographs, and a printing of the two negatives in register would likewise not show the detail desired. Thus, it is evident that some subjects cannot be satisfactorily illustrated by the usual procedures. In photographing Fig. is the light was subdued and, during the entire exposure of 75 sec., the analyzer nicol was rotated uniformly in its mounting from a crossed position to 45° uncrossed position to introduce the desired amount of contrast in the various individual quartz crystals. The true reproduction of the character and association of the iron oxides, and the additional structure and detail in the quartz areas, is apparent. It might be

Jan 1, 1946