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By N. L. Carwile, G. W. Geil

A metallographic study was made of deformation twinning (Neumann lamellae) in ingot iron slowly deformed in tension at —196O and —150°C. The results showed that twinning is initiated mainly during the initial stages of plastic deformation. However, the breadth of the twins generally increases with increase in strain up to fracture of the specimen. HE results of an investigation of the effect of low I temperatures on the flow, fracture, strain hardening, and strain aging characteristics, and the true stress-strain relationship for specimens of ingot iron deformed in tension were reported recently.1,2 In that study specimens of ingot iron, in different initial conditions, were slowly deformed in tension at various temperatures between —196" and +100°C. A phenomenon observed, but only briefly reported, was the formation of deformation twins (Neumann lamellae) in the specimens deformed at the lower temperatures. Preliminary metallographic examination of these specimens indicated that there was apparently some correlation between the deformation twinning and the strain of the specimen and that this factor merited further investigation. Some recent investigations have indicated a direct association of Neumann lamellae and the fracture of the metal. Bruckner".' * postulated that the twinning immediately precedes the fracture and the latter is initiated by the stopping of the propagation of twins, either at subgrain boundaries or at other structural features. Tipper and Sullivan5 postulated that Neumann lamellae are initiated by the shock or a shock wave set up at fracture in the still highly stressed unbroken metal, and that a high rate of deformation is a necessary condition for their formation. An extensive metallographic examination, therefore, was made of many of the specimens used in the study of ingot iron at this Bureau and of additional specimens deformed to selected strains under various conditions. The present paper summarizes the effects of deformation under these conditions upon the breadth and scope of the deformation twins. Other features of twinning will be discussed in another paper. Material and Testing Procedure All of the specimens were prepared from one lot of ingot iron, as hot-rolled, of chemical composition other than iron as follows: C, 0.02 pct; Mn, 0.02; P, 0.005; S, 0.018; Si, 0.002; Cu, 0.10; 0, 0.058; and N, 0.002. Cylindrical tensile specimens with a 2 in. gage length were used. The reduced section was slightly tapered from each end; the diameter (0.438 in.) at the midsection of the gage length was about 0.003 in. less than at the ends. The specimens were finished to the final dimensions by grinding and polishing in the axial direction. The ends of the specimens were machined with 3/4 in. x 10 threads and the shoulder fillets were machined to a radius of 0.75 in. The specimens were extended slowly in tension (deformation rate less than 0.5 pct reduction in area per minute) while immersed in an appropriate cryogenic liquid maintained at the desired temperature. The minimum diameter of the specimen was measured during the test by means of a specially designed reduction of area gage accurate to 0.0001 in." A detailed description of the testing equipment and the method of maintaining the desired temperature is given in a previous paper.' Each specimen, after deformation to a specified strain at a selected temperature, was sectioned longitudinally and examined metallographically. The preparation of specimens for metallographic examination was carried out in the usual manner by mechanical polishing and etching. Results and Discussion Deformation twins in specimens of ingot iron extended slowly in tension at —196" and —150°C are shown by the representative micrographs of Figs. 1

Jan 1, 1954

By Oliver C. Ralston, Foster Fraas

INTRODUCTION ELECTROSTATIC methods of separation are used only when some peculiar advantage is gained. Such cases are minerals that are not separable by differences in specific gravity or magnetic response and that are desired in particles as large as 10-mesh, a size on which flotation separation is inefficient. This paper covers several separations of this type and others. It includes studies in the electrostatic behavior of kyanite, sillimanite, and zircon, simple silicates that cannot be called either acid or basic but are more nearly neutral. Kyanite and sillimanite are both desired in 10-mesh size and are difficult to beneficiate from low-grade ores to give that type of concentrate. A separation of garnet from diopside was studied because this mixture had been removed from a wollastonite product by drying and magnetic separation, and no special or extra-preparation for electrostatic separation was necessary. THE SEPARATOR The separator used in these tests is of the nonhomogeneous field type shown in Fig I[a]. It consists of a 11.4-cm-diam rotating metal roll 2 at ground potential over which the dry mixture of minerals is fed. The roll serves as one electrode of the separating field, and the other electrode is that of 3, a smaller 5-cm-diam rotating metal cylinder which is held at a high direct-current potential. In this paper the term "electrode" will be confined to the electrode at 3, roll 2 being designated only as "roll." [ ]

Jan 1, 1947

By Charles Barrett

SINCE 1925, when the preferred orientations in compressed aluminum were first determined1, 2 the orientations have been described as a fiber texture in which a face diagonal, [110], of the face-centered cubic lattice is parallel to the compression axis. Subsequent experiments have seemed to confirm this texture,3-5 and a number of theories (recently summarized in references 6 and 7) have been proposed to explain it and to relate it to the behavior of single crystals during compression. 3,8-11 The experiments reported in this paper prove that the orientations are not adequately described as quoted above-i.e., as a [110] fiber texture-although this is a first approximation to the actual texture. They also show that the texture cannot be thought of as a stable orienta-tion that is reached and maintained after a sufficient amount of deforma-tion. The actual texture, when studied in detail at successive stages of compression, indicates that a hitherto unsuspected range of orientations is present, both in the polycrystalline metal as a whole and in various individual grains in its interior, and that a state of dynamic equilibrium exists within this range. The reasons for the failure of previous theories to predict the actual texture become obvious when the heterogeneous nature of the flow is considered. In addition to the deformation texture, the manner of its develop-ment, and its theory, this paper presents data on the following related subjects: the identity of strain markings in aluminum; the orientation changes in aluminum single crystals during compression and a com-parison of these with the conditions in individual grains of a polycrystal-line specimen; the origin of asterism in deformed single crystals, which heretofore has been regarded as a distortion localized at the surfaces of slip planes; and the relation of plastic strain in individual grains in an aggregate to the strain of the whole.

Jan 1, 1939

By V. Koump, T. F. Perzak, R. G. Olsson

Jan 1, 1965

By William Metcalf

It is the object of this paper to oppose unnecessary changes, and the introduction of new and confusing terms. From the earliest times of which we have ally record on the subject, iron has been divided into general classes. Whether iron was first known in the form of wrought iron or of steel, is a matter of no importance; but at the time when cast iron first became a prominent article of commerce, wrought iron and steel were old products— steel, at that time, being generally made from wrought iron by the process of cementation. As steel was then properly defined as iron containing more carbon than wrought iron, so cast iron was appropriately defined as iron containing more carbon than steel. Until the year 1776, when Huntsman first began the manufacture of a new kind of iron by melting wrought iron and steel in crucibles, the above definitions were all that could be desired. At first, probably, owing to imperfect appliances, only a highly carburized iron was melted in crucibles, and this led to its being called cast steel. If our ancestors had found a name for this material not involving the use of the word steel, we would have been saved the trouble of the present discussion. As the arts developed, new uses were found for steel, and the products of the crucible were varied, until at the present day it is quite common to find steel containing no more carbon than average wrought iron, and other steel containing nearly or quite as much carbon as some cast iron. All of these various products of the crucible have retained, or received, the name cast steel, usually abbreviated to the simple word steel, without caus-ing any confusion among producers or consumers in regard to terms or their meaning. In 1865, twenty-one years ago, the Bessemer process was introduced ; this was followed in a few years by the Siemens-Martin process, and the products of both were at once, and have ever since been, called steel, from the fact that they were identical in chemical and physical properties with crucible cast steel. At the present time, then, we have three subdivisions of cast steel, viz.: Crucible cast steel, Bessemer cast steel, and Siemens-Martin,

By Albert Sir Kitson

THE manganese ore deposits of the Gold Coast, British West Africa, occur in very ancient rocks, of both sedimentary and metamorphic types. In. certain respects, they strongly resemble those of India and Brazil, as contrasted with those of Tertiary age in Georgia. Viewed from the present condition of the maganiferous rocks, the oldest deposits are in the sediments. Later than these are the progressively metamorphosed representatives of these sediments; youngest are the products of decay and degradation with the concentration of manganese oxide of both areas. The oldest occurrences are in argillaceous and siliceous phyllites and slates, which show only a moderate amount of metamorphism. They belong to a series which also includes mudstones, sandstones, grits, conglomerates and subordinate limestones, with tuffs and lava-flow's largely of basic types. To this series I have given the name Birrim. Its age is unknown, for no definite fossils have been discovered in it. As the characteristics of these non-fossiliferous strata at many places are the same as those of strata in many parts of the world that are suitable for the preservation of fossils and that contain them, it is assumed that the Gold Coast deposits are pre-Cambrian. These rocks of the Birrim series have normally a northeast-southwest strike and are folded, but not to any very great degree except in certain belts. From the Eastern Province of the Gold Coast they may be traversed across their strike for more than 600 miles to the extreme northwestern corner of the Northern Territories. Thence they probably extend much further into French Territory.

Jan 1, 1927

By Murray F. Hawkins

Horner1 and van Everdingen8 ave shown that the pressure drop within the wellbore, as a result of having produced the well at a constant rate q for time t, where t is sufficiently large, is: van Everdingen observed that better agreement between theory and well performance can be obtained if, instead of assuming the permeability is kc everywhere about the well, it is assumed the permeability near the well-bore is substantially reduced as a result of drilling, completion and/or production practices. In order to account for the additional pressure drop he introduced the dimensionless quantity S, the skin effect factor, so that Eq. 1 becomes: Eq. 2 might have also been obtained as follows. Assume a zone of altered permeability k, exists about the well out to a radius r and beyond that the unaltered, external permeability k. The additional pressure drop required to overcome this skin of reduced permeability may be calculated with sufficient accuracy using the incompressible flow equation; for Browns-combe and Collins1 have shown almost no difference between compressible and incompressible steady-state flow, in the vicinity of the wellbore, and the small volume of fluid in the vicinity of the wellbore makes unsteady-state mechanics unnecessary. Then. The sign of this skin pressure drop will be positive or negative depending upon whether the altered permeability k, is smaller or larger, respectively, than the external permeability k... Adding the pressure drop of Eq. 3 to Eq. 1 to find the total pressure drop: Comparing Eq. 4 with Eq. 3 it is seen that the skin effect may be defined by: be determined from pressure build-up tests1,3,4,5,6,7,8 The average permeability kavg including the altered and external permeabilities, can be determined from PI tests, and may be defined approximately on the basis of steady-state flow, as was done by Thomas' in defining the damage factor, by: The productivity ratio is the ratio of the average to the external permeability, kavg/ke or This equation shows that the productivity ratio and the skin effect are not uniquely related, because of the uncertainty in the drainage radius, and also, in many instances, the wellbore radius. Fortunately, they enter in the logarithm. The curves of Fig. I are plots of Eq. 8 for values from 100 to 50,000. The points represent the skin effects and corresponding productivity ratios from a large number of well tests, taken from Fig. 15 of Ref. 5 or Fig. 13 of Ref. 9. While some of the data

Jan 1, 1957

By William Newnam

THE smelting of galena in the ore hearth has been practiced in many countries for several hundred years with varying success. In the United States the water-jacketed American hearths and the Jumbo hearths have found some favor, in the Missouri lead belt, where large quantities of non-argentiferous galena concentrates are produced. In form and method of operation the ore hearth has changed but little since its earliest conception. A detailed description of the furnace is not needed here; it has been fully described in most works on the metallurgy of lead and in many technical papers. Since its field is restricted to non-argentiferous galena, containing over 68 per cent. of lead, its .use is limited to a few districts; and, on account of certain disadvantages attending its operation, modern sintering and blast-furnace practice has nearly driven it out of the Missouri field. It is not generally known that the cost of producing pig lead is smaller by the hearth method than by sintering and blast-furnace smelting. Yet it is doubtful if any metallurgist knowing this to be true would recommend an American hearth installation-by reason of the disadvantages which will be briefly enumerated. The furnace has been limited to a length of from 4 to 5 ft., requiring for its operation two men working an 8-hr. shift as a maximum. The product per man is small; the work is hot and laborious; and the difficulty of completely removing the dust and fume has made it a notorious source of lead poisoning. Although suitable, for, operations on a small scale a large number of hearths would be required for a plant smelting 10,000 tons of 68 to 70 per cent. concentrates per month; and the number of semi-skilled laborers would be six times the number of hearths-a condition which is prohibitive. On account of the high percentage of dust and fume produced, a large flue and bag-house installation is required and, in the past, the handling and re-treatment of. this dust and fume has been a serious problem.

Jan 10, 1915

Efficient energy utilization in the electrolytic zinc process, relative to other zinc processes, is one of the reasons for its wide adoption in recent years, says John D. Siddle, zinc plant superintendent at the Bunker Hill Co., Kellogg, Idaho. Designers and operators of electrolytic zinc plants have pioneered process improvements, new equipment, and operating techniques to conserve energy. As energy costs increase it the future and competitive pressure mounts against less-efficient producers, these energy-saving improvements will he regarded as necessary for economic survival. Plant designers and operators should not lose sight of the savings in operating costs possible through intelligent utilization of all available forms of energy.

Jan 11, 1977

By Andres M. Liebenthal, Jan M. Mutmansky

This paper is concerned with the layout of a conveyor and beneficiation plant system involving several mines and a single point of delivery. The objective of the procedure is to locate the conveyor lines and beneficiation plants in an optimal manner considering the economics of scale inherent in both the transportation and beneficiation processes. Upon completion of the mining plan, the layout of the conveyor network is achieved through the principle of Steiner minimal trees. The optimal number and location of beneficiation plants for this layout are then determined using a sequential economic analysis based upon the flow of material from the individual sources to the ultimate destination. The practical aspects of the method and the advantages and disadvantages of its use are discussed to link the model to a practical problem.

Jan 1, 1976

By T. B. Brooks

THE iron ores of the Marquette region are mostly extracted in open excavations ; hence the process is more properly quarrying. Several attempts at underground work have been made, which have not, on the whole, been successful. The Edwards mine has been almost entirely wrought by candle-light. The slate ore pit, No. 1, of the New England mine, is now worked in the same way, as is also the Pioneer furnace pit of the Jackson mine. The Champion mine was opened systematically for underground work, with two levels, 60 feet apart, and three shafts at distances apart along the bed. of 200 feet; but this idea has been practically abandoned, the greater part of the ore in that mine being now taken out in open pits. Several other mines have occasionally worked underground stopes, but only temporarily; if such stopes could not be opened out to day-light, they have usually been abandoned. In brief, it may be said that no considerable amount of ore has as yet (1870).been extracted underground in the region, and of that so mined very little has been taken out at a profit; and I may add that it seems to be the belief of the most experienced mining men that this state of things will hold for some time to come for reasons which will appear. Nearly the same remarks may be applied to the mines of the Iron Mountain region, Missouri, the ores of which are very similar in character to those of Marquette. Some of the New York and New Jersey magnetic deposits are wrought open, but this is the exception, underground mining there being the rule. The following brief sketch of the geological structure of the Marquette deposits will indicate some advantages of the method of mining employed. The iron-bearing (Huronian) series of rocks, are stratified beds, the principal ore formation being overlaid by a quartzite, and underlaid by a diorite, or greenstone. This ore formation is made up, first, of pure ore ; second, of a mixed ore" (i. e., banded * A second part of this paper was read before the American Society of Civil Engineers. Both papers are embraced in Chapter IX, Part I, Vol. II, Geological Survey of Michigan.

Jan 1, 1873

By W. H. Bassett, J. C. Bradley

Beads of metal frequently appear at the ends of cast-copper wire bars and on the sides of wedge cakes near the top. These are richer in cuprous-oxide than the rest of the casting. A micrographical study of these exudations has been made. 11 is suggested that the materical is forced through the surface while the copper is solidifying. If not eliminated in process of manufacture, it shows on the finished polished sheet copper in patches differing in color from the main body of the shad. Figures 1 to 4 show the copper exudations, at different magnifications, as they appear on the ends of cast wire bars, and on the sides, usually near the top, of wedge cakes. Sometimes the exudations are in fine "drops;" at other times, large masses of the material are found. Microscopic examination of the copper exudation indicates that it is high in oxide and of eutectic proportions. Because of the difficulty of securing a suitable sample, the protuberances have not been analyzed chemically; but the spectroscope shows no indication that there are any more metallic impurities present than in the balance of the copper. The lowest copper plus silver content of the coppers studied for this paper was 99.914 per cent.; the highest, 99.966 per cent.; so the oxygen content of the whole casting would be well under 0.07 per cent. Structure of Protuberances The segregation of oxide between grains in the interior of the cast bar, not far from the "set," is shown in Figs. 5 and 6. In general, the amount of cuprous oxide begins to increase at a point about 0.01 in. below the normal surface of the casting, i. e., the base of the drop; but it does not attain maximum concentration in the main body of the metal. Vertical sections, Figs. 7 to 12, show that there is a definite line of large cuprous-oxide globules at the base of the drops. Horizontal sections at this place show that these large globules lie in a thin billowy

Jan 1, 1926

By R. F. Shurtz

This note calls attention to a contradiction in current eatistical theory and to corresponding difficulties in practice. These are significant concern in evaluating almost all ore deposits. The theoretical contradiction is that the commonly used spherical model for the semivariogram is not consistent with the usual definition of a "regionalized variable" as a mathematical function, the direct study of which "is excluded because its spatial variability is usually extremely erratic, with all kinds of discontinuities. . ." (Journel and Huijbregts, 1978). Specifically, this means a grade function that is too "rough" for interpolation to be useful. The practical difficulty is that the spherical semivariogram interprets the data upon which it is based in a manner that is, more often than not, demonstrably inconsistent with reality. This is attributable to the widely disregarded interaction between the sample pattern and the grade function. Each sample pattern "blurs" the grade function in its own particular way. It is as though the grade structure of the deposit were seen through a lens of poor resolution or reflected in a warped mirror, such as those found in amusement parks. The fitted spherical model embeds this sometimes dangerously blurred and distorted image in the Krige regression. A full analysis of these inconsistencies is to be presented later but, in the meantime, it seems urgent to communicate their effects so that those engaged in estimating ore reserves may be on guard. The spherical semivariogram has a sill and can be replaced by the corresponding covariogram. The equation of the spherical covariogram in normalized form, that is, variance and range both equal to one, is represented as: [ ]

Jan 1, 1984

By C. K. Leith

WE face the postwar problem of the use of minerals as sanctions to control the armament and the re-armament of the Axis powers at the source, minerals being the raw material of armaments. That is the subject of today's discussion. It is one thing to talk about controlling minerals in the interest of rearmament, and it is another thing to put any such ideas into effect. A provision for min- eral sanctions-not by that name but under broader terms-was contained in Article 16 of the League of Nations, and an attempt was made to apply min- eral sanctions when Italy cut loose in Africa. That was a failure because the plan was badly thought out. They did not have the right minerals included in the list. Also, they did not have the machinery set up at all. Somebody said to the League of Nations: Let's apply the sanction, and it was assumed that that was all that was necessary. It turned out to be a rather sad perfor- mance. However, that certainly cannot be taken as an example of what will happen if a properly thought-out pro- gram is adopted.

Jan 1, 1944

Mining examinations are of several kinds and the scope of the investigation depends in each case upon the purpose for which the examination is made. A formal examination of a developed mine is an expensive undertaking; from one to several months are allowed for the work according to the size of the property; many samples are taken; investigation is made of the geological features, including, perhaps, a topographical and geological survey of the surface; the metallurgical treatment of the ore is studied; finally, a determination of costs is demanded. Formal examinations are made for prospective purchasers or as a basis for the consolidation of several properties, and occasionally, in the owner's behalf, to verify the work of resident engineers, or to determine the readiness of a mine for equipment and the kind and capacity of equipment it shall receive. A formal examination of a mine should not be undertaken until a preliminary examination has shown that it is justified. It is regrettable that some engineers are in the habit of prosecuting long and exhaustive examinations of properties whose lack of merit should be, and perhaps is, apparent from the start, or of continuing their investigation long after an unfavorable result is seen to be inevitable. This wasting of a client's money is a species of trickery difficult to prove, and therefore the more contemptible. Preliminary examinations are precisely what the term implies, and are undertaken to determine the advisability of making

Jan 1, 1932

By L. Bombardieri, H. F. Mills

IRON KING mine, producing gold-silver-lead-zinc ore, is 10 miles east of Prescott, Ariz. At present the 1806 level is being developed. The echelon pattern of ore deposit continues at depth but is less pronounced, and the orebody is now more or less continuous over 2600 ft of strike length. with widths 5 ft to as high as 26 ft where overlapping of lenses occurs in one section of the mine. Better continuity of ore at depth has encouraged systematic mining and improved plant facilities to offset higher operating costs. With favorable persistence of ore at depth. the three-compartment No. 6 hoisting shaft appeared inadequate to handle increased tonnage from greater depths, and in 1952, a four-compartment steel and concrete shaft was started. This is now at a depth of 1906 ft, and shaft pockets and loading cartridges are being installed on the 1806 level. Ore from the new shaft, hoisted in 51/2 -ton Jeto bottom dump skips, is dumped into a 500-ton shaft bin, from which it is fed to a 16x30-in. gyratory crusher and conveyed 415 ft through an undersurface concrete gallery to the secondary crusher and conveying system supplying the 900-ton mill. Lead, zinc, and pyrite concentrates are floated, and the flotation tailings are cyanided after desliming. Waste from the new shaft is dumped into a 250-ton surge bin, fed from this bin to a 24-in. conveyor, and discharged into the glory hole above the block cave. The new shaft is served by a double-drum 400-hp hoist used for ore and waste; the No. 6 shaft conveys men and material To secure a cheap source of waste fill for stoping operations, a block cave area was undercut In the hanging wall near the north end of the mine above the 600 level. Waste from the block cave is drawn from any of three large drawpoints on the 600 level, and a series of hanging wall transfer raises with controls and bypasses on each level provide a fast low-cost material for fill. The block cave is worked vertically through to surface in the form of a steep-sided hole 350x250 ft and several hundred feet deep, the sides of which cave and provide fill material without any blasting. Fill is a mixture of caliche-cemented surface gravel and small particles of hanging wall schist. Level Development: An orebody 300 times as long as it is wide requires a lot of development work. Former practice consisted of driving a haulage drift about 30 ft from the ore in an andesitic footwall, a drift on the ore, and crosscuts from the haulage drift at 100-ft intervals. Crosscuts are about 90 ft long. At present, only the odd numbered levels are so developed, and on the even numbered levels only the haulage drift and crosscuts are driven. Little or no timber is used for this development. This change resulted in 20 pct reduction of development costs and 50 pet reduction of square set stoping required for removal of floor pillars. Elimination of ore drifts on alternate levels leaves

Jan 1, 1957

By Dr. O’Neil Thomas J., Donald W. Gentry

"We should be concerned about the future be- cause we will have to spend the rest of our lives there. " -Charles Kettering INTRODUCTION Since the early 1970s, there has been no economic phenomenon that has been more widely discussed or experienced in the United States than inflation. Al- though its precise definition and measurement are elusive, inflation has had pro- found and extensive impacts on the manner in which nearly everyone lives. It is painfully obvious to consumers that inflation is characterized by a continuing up- ward spiral of prices. In a capital-intensive industry like mining, those increases can be positively breathtaking. An interesting example is shown in Table 1. Table I shows that on a unit basis, the equivalent 1980 capital cost of Cuajone was over six times the cost of the adjacent and quite similar Toquepala operation completed in 1959. Such sobering statistics weigh heavily on the minds of executives who are contemplating major investments in new mining facilities. In spite of its monumental presence, inflation has usually been either inadequately covered or totally ignored in textbooks on engineering economy. The reasons for this are not entirely clear, but a contributing factor is the inherent difficulty in accurately predicting inflation. However, under certain conditions, inflation may become the most important factor in a mining investment, and it can rarely be safely ignored in capital investment analyses. DEFINING AND MEASURING INFLATION Defining inflation and related terms is relatively easy. Its measurement, how- ever, is the source of almost endless debate in economic and political circles. How- ever, much of that debate is not relevant to the scope of this book, so that only those issues which impact directly on the capital investment decision are covered in this section. Inflation is the general decline in the value of money as measured by what it will buy. It is clear, then, that the rate of inflation varies with the particular currency under consideration as well as the type of goods and services being purchased. One would find, for example, that the general rate of inflation relative to German marks

Jan 1, 1984

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Harry J. Morgan

One of the greatest improvements in drilling equipment has been the development of hard facing metals which are welded by electricity or by acetylene to form a facing which protects the steel of the bit from abrasive wear. The main desirable characteristics of hard facing metals are resistance to abrasive wear, resistance to shock and perfect bond with underlying metal. Resistance to abrasion offered by various metals shows many anomalies. Compounds containing carbon, silicon and boron are the most important hard substances. Carbon, as diamond, silicon carbide and especially the carbides of iron, chromium and tungsten are the outstanding hard products in common use. Tungsten carbide is probably the most commonly used. It is made in the electric furnace and it is important to get the right amount of carbon and the correct crystalline structure in order to obtain the greatest hardness and greatest resistance to abrasion. It may be obtained in three main divisions: wrought, cast and casehardened. Insert hard metals are common. The method of application varies, but it is generally welded to the bit, placed in channels or in drilled holes and covered with a hard surfacing metal. Robinson' has given a very complete article on the use of inserts. Gregg and Küttner2 has discussed the metallography of tungsten carbides and given a good bibliography of the subject,. The time and expense of large-scale testing, together with variations in results, led to the development of a laboratory testing machine for determining the abrasive-resisting qualities of different metals. This machine consists of a motor-driven 40-grain, alumina-base corundum wheel, 8 in. dia., rotating at 30 r.p.m. It is run wet and dressed with

Jan 1, 1930