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By Will Mitchell

The classical definition of a beneficiation engineer as one who treats an ore in order to separate and discard worthless fractions by essentially physical means is obsolete. Technology in the profession has advanced so rapidly during the last two or three years that educators have not been able to coin definitions to keep up with the pace. In the past some people have hesitated to include leaching or even agglomeration as minerals beneficiation, because of the major chemical changes involved. This view has fallen by the wayside, especially because a majority in the profession have become actively involved in extraction and pyro processes that go far beyond the original definition of mineral dressing. To say that there is a great revival of interest in leaching is putting it mildly, for the uranium business, like the gold business, now depends almost entirely on leaching. This revival of leaching, long overdue in mineral engineering, has been stimulated this year, especially as a result of the relaxation of security restrictions surrounding the recovery of uranium from its ores. It has brought new unit operations to minerals beneficiation, namely ion exchange and solvent extraction. These operations have appeared as resin-in-pulp, solvent-in-pulp, and liquid-liquid systems. In many cases these leaching and separation procedures, now reaching the production stage, have been engineered by minerals beneficiators. The trend toward leaching has also had impact on the technology of beneficiating other nonferrous minerals, especially copper, manganese, columbium, tantalum, nickel, cobalt, titanium, and the rare earths.

Feb 1, 1956

By M. F. Williams, L. G. Hendrickson

In classification of pulps bearing magnetized ferro-magnetic particles, depolarizing is of great importance. If size separation is to be effective, particles must be individual rather than in flocs. Depolarizing is also practiced in heavy medium separations in which ferrosilicon or magnetite is the medium. When particles of ferromagnetic material have been removed from a magnetic field, residual magnetism causes agglomeration. The term depolarizing refers to the operation of reducing or eliminating this residual magnetism and may thus be considered magnetic deflocculation. The terms demagnetizing and randomizing are also used.

Feb 1, 1956

By Elmer A. Jones

Like the caboose on the end of a long freight train L made up of mineral and metal processing and consuming industries, the mining industry progresses according to the movement of the train to which it is coupled. Sometimes the caboose rolls smoothly; occasionally it bumps along on the ties; almost always it is under criticism from someone for being too small, too large, too expensive, foolishly progressive, or hopelessly out of date. We who ride in the caboose are used to the rough by now, but it is nice now and then to have a bit of the smooth. Last year the train of industrial production rolled ahead swiftly and smoothly, and, except for a hot-box caused by strikes in copper mines, so did the caboose. As is brought out elsewhere in this issue, the outlook for 1956 is for more of the same.

Feb 1, 1956

By H. V. W. Donohoo

Exploration in 1955 was marked by a trend toward large-scale programs using a number of geophysical techniques. These programs were initiated both to locate new mineral districts and to bring individual prospects into production. All 14 companies replying to the author's questionnaire include geophysics in the general exploration routine whenever it is applicable, and five companies carry on extensive geophysical programs. Nearly all report that company personnel perform the surveys. In addition to these firms there are the many smaller operators who contract much of their geophysical work. There are indications that the volume of such contracting is sizable.

Feb 1, 1956

By S. M. Brisbane

The life of refractory linings in rotary cement kilns can be shortened by uneven or inadequate support of the kiln and its shell and by variations in the conditions of operation. Alteration of these factors may, according to their nature, bring about mechanical deterioration of the lining or promote chemical attack. Chemical attack has been described elsewhere. The distortion of cement kilns has been discussed in a general manner by Rochow, who indicates the amount of distortion which may occur in an unlined shell, and by Rosenblad; who states that the deformations of the shell are greatest above the trunnions. The present article indicates the extent of the distortion of a kiln to an oval shape in certain selected positions and the deviation from a straight line of the kiln along its length between two supports. The cement kiln is a long, hollow, rotating cylinder consisting of steel plates which may be either welded or riveted together. This shell is supported on tires, frequently 60 ft apart, which roll on trunnions. The large mass of the kiln causes distortion of its cross-section; it becomes slightly oval, i.e., diameters lengthen as they become horizontal and shorten as they become vertical. There is also a tendency for the shell to bow between supporting tires; this bowing may be upwards or downwards depending on the position of the weight forces and the supports. The extent of the deviations from the ideal kiln shape was investigated.

Feb 1, 1956

By John F. Barkley, J. W. Woomer, H. F. Yancey, H. B. Charmbury

The coal picture in 1955 was much brighter than in 1954, when the tonnage produced dropped to the 1939 level. Bituminous coal and lignite production are expected to approach 465 million tons, against 392 million tons in 1954, an increase of about 19 pct. On the other hand, the production of anthracite declined about 7 pct to some 25 million tons. There was marked improvement in coal consumption in all industrial lines except railroads. At the end of November 1955 the largest consumer, electric power utilities, had used about 126 million tons, an increase of some 22 million tons over the previous year. Coke-oven consumption increased about 19 million tons and coal coked in beehive ovens increased about 1.5 million tons, due to heavy coke

Feb 1, 1956

By John Gittins

Lots 11 and 12, Range IX, Calumet island, are underlain by a Grenville metamorphic complex into which sills of tourmaline granite pegmatite have been injected. The pegmatite has an average mode-potash feldspar 65 per cent, sodic plagicdase 10 to 20 per cent, quartz 5 to 20 per cent, tourmaline 10 to 15 per cent, accessory minerals < 5 per cent; it is unzoned except for a narrow border zone. Some of the feldspar has been replaced by calcite. Microcline has been ?partially replaced by sodic plagioclase. Three varieties of tourmaline are present (black, blue, and green) and spectrographic analysis suggests progressive compositional changes during its crystallization. The presence of U- and Th-bearing minerals in the pegmatite prompted the Quebec Nickel Cor,porat10n, Ltd., to explore the possibility of developing the pegmatite but it does not appear that this is economically possible at the ? present time. Tt\e Grenville metamorphic complex consists of recrystallized limestones and calcsilicate rocks of the albite-epidoteamphibolite facies and the amphibolite facies, which were derived from sedimentary rocks. Several of these are dis-equilibrium assemblages, and retrograde metamorphism has probably formed biotite and epidote from hornblende. The schistosity of the gneisses dips steeply eastward. Numerous strike faults are roughly parallel to the schistosity and one of the pegmatite sills is bounded by such a fault, dipping at 60 ° with about one foot of fault breccia. The general structure of the map-area seems to be an asymmetrical syncline ?overturned to the west. The emplacement of the pegmatite is associated with a period of folding, metamorphism, and igneous intrusion.

Jan 1, 1956

By R. L. Slobod, B. H. Caudle, R. A. Erickson

In predicting the sweepout pattern efficiency to be expected in a .secondary recovery operation, the reservoir engineer is often confronted with a situation in which part of the producing formation lies between the last row of wells and the reservoir boundary. To date, there has been little or no reference in the literalure to sweepout pattern efficiencies in such areas. This paper presents the results, of a laboratory study in which the area contacted around the edge of a reservoir injected in a five-spot pattern was determined. The X-ray shadowgraph technique was used in this study. It was found that surprisingly large portions of the reservoir area lying outside the well network are conracted by the injected fluid before, abndonment conditions are reached. In fact, it can he said that at least 00 per cent of the circa lying outside the last row of wells and within a distance of one well spacing of these wells will ultimately be contacted by the injected fluid in the case of most water floods. Frorn the results given in this paper, it is possible to estitilate not only the extent to which encroachment into these areas will occur but also the injection volume necessary to produce the wells to abnndonment conditions. INTRODUCTION While considerable work has hern done in recent years1.?.&apos;.&apos;&apos;.&apos; evaluating the fraction of the reservoir contacted as a function of the mobility ratio for several different well patterns, there has been practically no mention of what happens to the oil in that portion of the reservoir which lies between the last row of wells and the reservoir boundary. In fact, the assumption is generally made that little or no recovery can he expected From this area. This assumption is incorrect and in many cases will lead to seriouq errors in calculating reservoir performance. The fraction of the area outside the regular well pattern contacted in a five-spot injection system has been studied using the X-ray technique5 to follow the progress of actual floods in porous models of reservoir elemental areas. In this paper, the method for carrying out such a study and the results showing the fraction of the area in question swept as a function of mobility ratio and the produced fluids are presented. THE REPRESENTATION OF A RESERVOIR BY ITS ELEMENTAL AREAS She portion of the reservoir lying between the edge of a reservoir and a line connecting the outermost wells may be roughly designated as the part of the reservoir outside the regular well pattern. An example of such an area is shown as the shaded portion in Fig. 1. The case of a square reservoir utilizing a five-spot injection program and with one full well spacing between the outermost wells and the boundary (Fig. 1) was selected as the single example which would provide the most insight into

Jan 1, 1956

By John R. Reynolds

This paper describes mining and milling methods of the American Smelting & Refining Co. at the Morning mine in the Mullan area of the Coeur d&apos;Alene mining region in Idaho and is one of a series of Bureau of Mines reports dealing with methods and costs of mining throughout the United States. The Morning mine has been described previously in a Bureau of Mines report published in 1930,2/ and the milling methods and costs at the Morning concentrator were presented in a Bureau of Mines report published in 1932. 3/ These reports are supplemented by this publication, which presents data to show the effect of changing times and conditions on a typical medium-size mining operation during the latter part of its history, when costs were rising and production was from increasingly greater depths. The report contrasts two periods in the history of the mine-periods not too far separated in years but considerably different in economic conditions. During the first period (1939) costs of labor and materials were moderate, mining operations were just being transferred from the main shaft to deeper workings opened from the offset shaft, and the operation prospered. During the second period (12 years later) production costs had increased following the national trend in all industry, mining was from greater depths near the bottom of the ore body, and the operation was becoming unprofitable. Mining on the lower levels of the property ceased in 1953.

Jan 1, 1956

By J. W. Fredrickson

VERY little information is available in the literature concerning the solubility of magnesium in titanium. Aust and Pidgeon&apos; report the solubility of titanium in magnesium to be 0.0025 pct at 650°C and 0.015 pct at 850°C. X-ray diffraction studies failed to detect any evidence of solid solubility. Based on the fact that the addition of titanium to magnesium increases the c/a ratio of magnesium, Busk&apos; suggested that the Mg-Ti system, like the Mg-Zr, is a peritectic. Eisenreich- eported the solubility of titanium in magnesium to be 0.003 pct at 655°C and 0.064 pct at 760°C. Removal of hydrogen from the melt increased the solubility of titanium to 0.115 pct at 800°C. Eisenreich proposes a peritectic-type diagram for the high magnesium side of the system. Recent work&apos; with Ti-Mg diffusion couples indicate that the solid solubility of titanium in magnesium is extremely small and that there is limited solid solubility of magnesium in titanium. Experimental work on the Ti-Mg system is complicated by the fact that the boiling point of magnesium is considerably below the melting point of titanium. Consequently, the usual alloying methods are impractical. Alloying was accomplished in this investigation by sheath-rolling compressed compacts." The alloys were made from titanium sponge and high purity magnesium. Chemical analysis of the sponge showed 0.04 pct Mg, <0.005 pct Al, <0.001 pct Cu, 0.05 pct Fe, 0.022 pct Mn, <0.0025 pct Ni, 0.007 pct Si, <0.005 pct V, and <0.01 pct Zn. All heat treating was conducted in a protective atmosphere by encapsulating the specimens in fused silica ampules under a partial pressure of helium. Equilibrium was achieved by holding the specimens at temperature for periods of 24 to 120 hr. The alloys were hot rolled, cold rolled, and annealed prior to solution heat treatment. Fig. 1 shows the constitutional diagram obtained for the Ti-Mg system up to 1.5 pct Mg. Oxygen was known to be present in the alloys; therefore, it is necessary to consider the alloys as ternary rather than binary and the diagram should be viewed as a plot of a section through the Ti-Mg-0 system. Other investigatorso have shown that the addition of oxy- gen to titanium stabilizes the a phase. The data presented in Fig. 1 indicate that the addition of magnesium to titanium tends to stabilize the p phase. Armour Research Foundation7 has shown that the addition of magnesium to zirconium lowers the a transus and is classified as a p stabilizer in that system. Magnesium is soluble in solid titanium to the extent of at least 1.5 pct in both the a and /3 phases. No intermetallic compounds or magnesium-rich phases were observed either by light microscopy or X-ray diffraction. However, this does not negate the possibility that such phases exist at higher alloy concentrations.

Jan 1, 1956

By Rudolph G. Wuerker

THE scarcity of values of tensile strength of rocks has been explained by the lack of successful testing procedures. In the case of mine rock a description is given&apos; of the difficulties encountered in testing a cylindrical specimen, such as a core, by conventional methods. Over a period of years the following method has given definite and reproducible results with the weakest as well as with the strongest rocks. It does not completely supersede the use of cores with special fixtures but is a supplement in all cases where cores cannot be obtained, as from soft rocks, or in cases where it is less expensive to prepare test specimens by cutting them out of the rock instead of drilling cores. Principle and equipment are the same as for the test for tensile strength of hydraulic-cement mortar.&apos; The test specimen, Fig. 1, has the shape of a briquet. While in the original cement mortar test the briquet is cast in a special mold, it is prepared from rocks in different ways, depending on how easily they can be cut and shaped. Soft rocks, which cannot be core-drilled with a carboloy or diamond bit, are simply hand-cut. Only two dimensions need be watched. The first is the 1-in. diam at the narrowest cross-section of the briquet. The other critical measure is the radius of curvature of the waistline, as the roller supports in the grips have a fixed distance. This radius is ground out of the solid by means of a carborundum grinding wheel having a 3/4-in. radius. Medium hard rocks can be core-drilled with a carboloy bit. The resulting core can be used for nondestructive sonic testing first, and after that for any destructive test. By using an EX-bit and by carefully placing the coreholes, preferably by using a tenplate such as shown in Fig. 1, it is possible to obtain from the rock a punched sample from which numerous tensile briquets can be made. The outside radius of the EX-bit differs from the radius of curvature of the briquet by 1/8 in., but this still permits placing and aligning the specimen in the grips. In the case of bedded rocks the core might have bedding planes normal to the plane of the briquets, and rocks can be tested in any arrangement of the bedding planes desired. Hard rocks, limestones, igneous, and metamor-whic rocks can only be diamond-drilled or diamond-cut. Here the method of getting the tension briquets by accurate placing of EX-drill holes is especially economical. The tops of the briquets made from hard rocks cannot be rounded; they are straight cuts made with a diamond cut-off saw and rounded off on a polishing wheel. Results: As long as specimens broke over the waistline the results were considered acceptable. Further statistical treatment of the tests&apos; showed a satisfactory percentage of standard deviation. The tensile strength values obtained by this method do not represent true values because of the stress concentration caused by the curvature of the side of the piece and because of the closeness of the grips. The ratio of maximum to average stress at the plane of failure has been determined to be about 1.75." All tensile strength values listed in Table I are corrected accordingly. To avoid this stress-concentration, if there are a sufficient number of cores, tensile strength can be measured by imbedding the cores in mortar in the two outer briquets in the gangmold.4 Strain-Measurements: The applicability of the briquet specimens for strain observations was tested in the case of sandstone and shale. Two element Rosette SR-4 strain gages were used. Young&apos;s modulus and Poisson&apos;s ratio, both in tension, were computed and found to be different from those in compression, determined during the same test series and from the same rock, see Table I. References 1 L. Obert, S. L. Windes. and W. I. Duvall: Standardized Tests for Determining the Physical Properties of Mine Rock. U. S. Bur. Mines R.I. 3891 (1946). 2 Test for Tensile Strength of Hydraulic-Cement Mortar, ASTM Standard C 190-44. S F. O. Auderegg, R. Weller, and B. Fried: Tension Specimen Shape and Apparent Strength. Proc. ASTM 11939) 39, pp. 1261-1269. 4 API Code 32.

Jan 1, 1956

By C. T. Wei, A. Kelly

USING a recently developed X-ray method, reported by Schulz,2 it is possible to make a rapid survey of the perfection of a single crystal at a particular surface. This technique has the advantage of allowing a large surface of a specimen to be examined by taking a single photograph and it compares well with other X-ray methods in regard to sensitivity of detection of small angle boundaries. During the course of a survey of the perfection of large crystals of aluminum produced by a number of methods, an examination has been made of a number of single crystals produced from the melt using a soft mold (levigated alumina)." Crystals grown by this method are known, from an X-ray study carried out by Noggle and Koehler,3 to contain regions where they are highly perfect. In the present work, it has been possible to obtain photographs showing directly the distribution of low angle boundaries at a particular surface of these crystals. single crystals were grown from the melt using the modified Bridgman method with a speed of furnace travel of -1 mm per min. These were about 1/10 in. thick, 1 in. wide, and several inches long. The metal was 99.99 pct pure aluminum supplied by the Aluminum co. of America. The crystals were examined by placing them at an angle of about 25° to the X-ray beam issuing from a fine focus X-ray tube of the type described by Ehrenberg and Spear4 and constructed by A. Kelly at the University of Illinois. A photographic film was placed SO as to record the X-ray reflection from the lattice planes most nearly parallel to the crystal surface. The size of the focal spot on the X-ray tube was between 25 and 40 u, and the distance from the X-ray tube focus to the specimen (approximately equal to the specimen to film distance) was -15 cm. White X-radiation was used from a tungsten target with not more than 35 kv in order to reduce the penetration of the X-rays into the specimen. Exposure times were approximately 1 hr with tube currents between 150 and 250 microamp. The type of photograph obtained from these crystals is illustrated in Fig. 1, which shows a number of overlapping reflections from the same crystal. The large uniform central reflection is traversed by sets of horizontal white and dark lines. These two sets run mainly parallel to one another. Lines of one color are wavy in nature and often branch and run together. Large areas of the crystal surface show no evidence of these lines whatsoever. The lines are interpreted as being due to low angle boundaries in the crystal, separating regions which are tilted with respect to one another. A white line is formed when the relative tilt forms a ridge at the interface and a black line is found when a valley is formed. In a number of cases, the lines stop and start within the area of the reflection and often run into the reflection from the edge, corresponding to a low angle boundary starting from the edge of the crystal. The prominent lines run roughly parallel to the direction of growth of the crystal although narrow bands can run in a direction perpendicular to this; see Fig. 2. Although they may change their appearance slightly, the lines tend to occur in the slightly,Same place in the X-ray image and to maintain their rough parallelism when the crystals are reduced in thickness by etching. Thus the low angle boundaries can occur at any depth within the crystal. The appearance of the lines is unaffected by subjecting the crystal to rapid temperature changes, such as plunging into liquid nitrogen or rapid quenching from 620°C. From the width of the lines on the x-ray reflection, values can be found for the angular misorienta-tion of the two parts of the crystal on either side of a boundary. The values found run from 1&apos; to 10&apos; of arc, but values of UP to 20&apos; have sometimes been found, e.g., the widest lines on Fig. 2. These mis-orientations are much less than those commonly found in crystals possessing a lineage structure. When a number of a and white lines occur, running in a roughly parallel direction across the image of a Crystal, the total misorientation corresponding to lines of one color is approximately equal to that corresponding to lines of the other color. The interpretation of the lines as due to low angle boundaries has been checked in a number of ways. Photographs taken with different specimen-to-film distances distinguish lines due to low angle boundaries from effects due to surface relief of the specimen. Normal Laue back-reflection photographs, taken with the beam irradiating an area of the surface showing a number of the lines, show white lines running through each Laue spot. Black lines are set to see by this method. X-ray photographs were also taken, using the set-up described by Lam-one et al.5 when the beam straddles regions giving rise to lines in the Schulz pattern, split reflections are observed within the Bragg spot. The misorienta-tions calculated from the separation of these reflections and that found from the widths of the lines on the schulz technique patterns show good agreement. An exposure was made with Lambot technique of an area of the crystal showing no evidence of low angle

Jan 1, 1956

Jan 1, 1956

By Paul Meadows

The Buckrange reservoir, Stephens field, Ark., is approaching the economic limit of production under present operating conditions. Over 100 million barrels of oil remaining in the reservoir will not be recovered by primary producing methods. The Bureau of Mines, in cooperation with the Arkansas Oil and Gas Com-mission, made the petroleum-engineering study presented in this report to aid operators in evaluating secondary-recovery possibilities in the reservoir and in planning secondary-recovery programs if their initiation is decided. The Stephens field, in Columbia, Nevada, and Ouachita Counties, Ark., is about 12 miles northeast of Magnolia, Ark., and 15 miles west of the Smackover field. Surface elevations in the area average about 240 feet above sea level.

Jan 1, 1956

By R. T. MacMillan

Many bench-scale tests and studies have been conducted in developing and testing a chloride-volatilization procedure Ear treating low-grade manganese ore from the Maple Mountain-Hovey Mountain deposit of Aroostook County, Maine. The ore, averaging 10 to 12 percent Mn, contains manganese in several forms and is resistant to concentration or extraction by usual physical and chemical procedures. Over 90 percent of the manganese, content of the ore has been recovered using a chloridizing roast in which the ore was heated at 950°-9b0&apos; C. in a circulating stream of hydrochloric acid gas. Chlorides of manganese and iron were volatilized and swept to a fume collector, where they were condensed and separated from the [as] stream. Operation of a small, 1-pound-per-hour shaft Furnace produced enough chlorides for studying other factors in an integrated process such as: (1) Conversion of the chlorides to oxides; (2) recovery of HC1 gas of suitable concentration Ear recycling to the chloridizer; and (3) control of the Mn-Fe ratio in the oxide product to produce a suitable feed for ferromanganese production.

Jan 1, 1956

By Bernhard Blumenthal

A melting process was developed by which high purity electrolytic uranium crystals can be converted into sound ingots without serious contamination. Careful preparation of the crystals, melting in a high vacuum, and directional solidification led to a metal of better than 99.993 wt pct purity. The metallographic examination showed a substantially clean metal with only residual amounts of a second phase which responded to heat treatment. The density of high purity uranium is 19.05 g per cu cm. FOR the study of the fundamental properties of uranium and its alloys, a base metal of high purity is needed, and an investigation was started at Argonne several years ago to examine various methods of preparing high purity uranium. Early success was achieved by the fused salt electrolysis process in preparing high purity metal in crystal form,&apos; and the problem became that of melting the crystals into ingots without contamination. The electrolytic crystals contained a few ppm of heavy metals, less than 15 ppm C, and large quantities of potassium and lithium in the form of trapped fused salt electrolyte. On melting in vacuo in magnesia or urania crucibles, the metal picked up considerable quantities of carbon and some iron, copper, and silicon but lost most of the potassium and lithium. It was not metallographically clean, and much research work was necessary to determine the optimum melting conditions for minimum contamination. This work has resulted in the development of a melting procedure by which sound ingots can be prepared with only a limited contamination by carbon. In the section entitled "Melting of the Electrolytic Metal," the equipment and processes that have been developed for melting the electrolytic crystals are described in detail. The "Metallography" section is devoted to the metallography of high purity uranium, and the section "Density of High Purity Uranium" contains the first property measurement on high purity uranium—a density determination. Melting of the Electrolytic Metal Apparatus—Melting and Vacuum Equipment: Uranium may be melted in either resistance or induction-type electric furnaces. Resistance heating was found to be preferable to induction heating for melting down the electrolytic crystals, for several reasons: Although induction heating permits fast heating, this advantage cannot be utilized when crucibles with limited thermal shock resistance are used. Temperature control of induction-heated melts is poor, and the stirring effect increases the rate of contamination of the melt from the crucible, slag, or the furnace atmosphere; liquation and controlled solidification are difficult to carry out. Because of these objections, resistance heating was chosen. A 10 kw Globar resistance furnace of low heat capacity permitted uniform heating of a uranium charge to its melting point in 45 min. The furnace was insulated with a removable aluminum shield so that, after melting and removal of the shield, the furnace could be quickly cooled to room temperature. The furnace was equipped with an apparatus for directional solidification; see Fig. la. The crucible was suspended in the center of the furnace; and when the melting was complete, the crucible was slowly lowered into the cold end of the furnace tube. Solidification took place upward from the bottom; and when the rate of lowering was small, a sound ingot free from sink holes and shrinkage cavities was produced. To remove the large quantities of gas contained in the electrolytic crystals, melting in a high vacuum is mandatory. While, from the standpoint of contamination, melting in a highly purified argon atmosphere appeared feasible, lithium and potassium removal proved less efficient under such conditions. Also, a vacuum-melted ingot has a cleaner surface than one melted in an inert atmosphere. The vacuum system must be of very high pumping speed and leak tight so that a vacuum of less than 2x10-7 mm Hg is attainable when the system is pumped down cold. The system must have a high pumping speed, so that the pressure maximum which may rise to 1x10-4 mm during heating can be quickly reduced

Jan 1, 1956

By A. L. Pranatis, G. M. Pound

Changes in length of copper foils of varying thickness and grain size were measured under such conditions of low stress and high temperature that it is believed that creep was predominately the result of interboundary diffusion of the type recently discussed by Conyers Herring. The surface tension of copper was calculated and results confirmed previous work within the limits of experimental error. Under the assumption of viscous flow, viscosities were calculated as a function of temperature and grain size. Predictions of the Nabarro Herring theory of surface grain boundary flow were borne out fully and the Herring theory of diffusional viscosity is strongly supported. ONLY a relatively few techniques for obtaining the surface tension of solids are presently available. Of these, the simplest and most straight forward is the direct measurement of surface tension by the application of a balancing counterforce. Thin wires or foils are lightly loaded and strain rates (either positive due to the downward force of the applied load or negative if the contracting tendency of surface tension is sufficiently greater than the applied stress) are observed. By plotting strain rates against stress, the load which exactly balances the upward pull is found and a simple calculation yields a value for the surface tension. The technique is of comparative antiquity, and solid surface tension values were reported by Chapman and Porter,&apos; Schottky; and Berggren" in the early part of the century. Later, the filament technique became fairly well established as a method for determining the surface tension of viscous liquids, and Tammann and coworkers,&apos;. " Sawai and co-worker and Mackh howed good agreement between the values of surface tension for glasses and tars obtained by the filament technique and by more conventional methods. With the increased confidence in the technique gained in these experiments, the method was applied to solid metals and the first reliable values of surface tension of solid metals were reported by Sawai and coworkers10&apos; " and by Tammann and Boehme." More recently, Udin and coworkersu-&apos;" have reported the results of experiments with gold, silver, and copper wires. Similar experiments with gold wires were carried out by Alexander, Dawson, and Kling.&apos;" The excellent review articles of Fisher and Dunn" and of Udinl@ should be referred to for detailed criticism of the foregoing work and for discussion of underlying theory. In all the foregoing calculations, it is assumed implicitly that the material contracts or extends uni- formly along the length of the specimen and also that it flows in a viscous fashion, i.e., that strain rates are proportional to stress. For an amorphous material, such as glass, tar, or pitch, the assumptions are quite valid and good agreement is obtained with values of surface tension measured by other techniques. The values reported for metals, however, are occasionally regarded with misgiving, since it can be argued that, because of their crystalline nature, true solids can not deform in a viscous fashion. If this is true, then the results reported for solid metals over a long period of years are of only doubtful value. Thus it is clearly necessary that a mechanism be established that would explain both the viscous flow and the uniform deformation that has been assumed. Such a mechanism has been proposed by Herring."&apos; Briefly, he suggests that, under the conditions of the experiment, deformation takes place by means of a flow of vacancies between grain boundaries and surfaces. This is a direct but independent extension of the theory proposed by Nabarro" in an attempt to explain the microcreep observed by Chalmer~.In a condensed form the Herring viscosity equation is TRL there 7 is the viscosity, T the absolute temperature, R and L grain dimensions, and D the self-diffusion coefficient. In its complete form, all constants are calculable and it includes such factors as grain shape, specimen shape, and degree of grain boundary flow. When applied to existing data, good agreement was obtained between predicted and observed flow rates. The theory received provisional confirmation from the work of Buttner, Funk, and Udin" who observed viscosities in 5 mil Au wire much higher than those in the 1 mil wire used by Alexander, Dawson, and Kling.&apos;" More significant were the completely negligible strain rates found by Greenough" in silver single crystals. Opposed to these observations were those of Udin, Shaler, and Wulff&apos;" who found indications of viscosity decreasing as grain size increased. Thus, complete confirmation of the theory was lacking in that the data to which it could be applied contained only a limited number of grain sizes. Hence, it was proposed that a series of experiments be carried out with thin foils of varying grain size up to and including single crystals, where, according to the Herring theory, deformation would occur only at almost infinitely slow rates.

Jan 1, 1956

By H. H. Rachford, W. P. Schultz

The use of computing machines to solve physical problems has made it imperative to represent physical data in a form computing machines can use. Although curve-fitting is an old and well-practiced art, there still seems to be some interest in questions regarding what methods can be used and why. Even though there are many good references on this subject, it may be of some value to discuss a particular method which has been found to be useful, and to make available the associated tables for its use in the hope that there can be saved a few of the tedious hours necessary to reduce many of the suggested methods to practice. Although a very brief discussion of the mathematical background of the tables is included immediately below, those interested only in their use can skip directly to the section on Use of the Tables. Direct Fit of a Set of Points A frequently encountered problem is: Given data which can be represented by a smooth curve +(x), to find an easy-to-evaluate function F(x), with only a few coefficients, which is a good approximation of +(x) on the interval 0 5 x 5 x,,. Consider F(x) as a linear combination of m + 1 arbitrary, single-valued, continuous, linearly independent functions, f,(x), Ff.r) = a,f,,(x) + a,f,(x) + . . . -+ aifi(x) + If the value of Q(x) is known or can be read from the curve at the points xj: +(x,), +(x,), . . . +(xj) . . . +(x.), and if n = m, then all the coefficients of F(x) can be determined, and F(x,) — +(x,) = 0 for j =. 0, 1, . . . n. This follows from the solution of the set of linear simultaneous equations. +(x<.) = aofu(x,) + aJI(x0) + . . . + a,,f,,(x,) =a, = f,,(x,) + a,f,(x,) + . . . + a,f,,(x,) +(x,,) = a,,f,(x,,) + a,f,(x,) + ... + a,,f.,(x,,) ...........(2) for the coefficients ai. Although the set a, from the solutions of the set of Equations 2 yields an fix) which gives an exact value of $(x,) for the n + 1 points, there is no restraint on ~(xj in the interval xi < x < xj+,. Indeed, if the points +(x,) are not sufficiently smooth, very serious differences may arise between F(x) in the interval and the smooth curve +(x). Least-Squares Fit It has been suggested&apos; that if n is made to exceed m, and the set a, is found to minimize the function the function F(x) is much less sensitive to small errors in +(xi), and usually provides a much better fit to the smooth function +(x). This is known as the best fit in the sense of the least-squares error. To minimize $, set £ = 0,i = 0,1,... iTi,.....(3) The m + 1 equations from Equation 3 are k—n k=n a.^p /,,(a) f,(xt) + a, X A: = 0 k=O k = n k = n k=0 k=0 +(x.) f,(x,),............(4) one equation being obtained for each i = 0, 1, . . . m. Inasmuch as the arbitrary functions f(x) may be evaluated for x,, k = 0, 1, . . . n, and the +(x,) are known values of the curve to be fitted, the simultaneous Equations 4 may be solved for the set a,. Particular Functions Given the functions fi(x) and the set +(xj), the solutions for require evaluating a number of sums of products as well as the solution of an m + 1 order set

Jan 1, 1956

By Paul B. Crawford, Bobby L. Landrum

Electrical model studies have been made of the effect of unsymmetrical vertical fractures on production cnpacity. The study war restricted to the case of two vertical fractures originating at the well and extending out into the reservoir for various distances and orientations. The ratio of the short fracture length to the long fracture length was varied from 0.1 to 1.0 in successive studies. The angle separating the two fractures was varied from 0 to 180 degrees. The most effective fractured patterns were obtained when the fractures were oriented 180 degrees. It was found that when the total fracture length was equal to 0.2 of the drainage radius, the increase in production capacity may vary from approximately 1.55 to 1.95. depending upon the ratio of the short fracture length to the long fracture length and the angle separating the two fractures. If the total fracture length were 0.5 of the drainape- radius. poroduction cavacitv., increases varving 1.95 to 2.65 were observed, depending on the angle between the fractures and the ratio of the .short fracture length to the long fracture length. The fractured well production capacity decreased aPproxin?ately I to 10 per cent as the angle separating the fractures was varied from 180 to 90 degrees. It was dependent on the particular fracture. The commercial application of reservoir fracturing techniques has caused an interest to be expressed in the effect of vertical and horizontal fractures on production capacities. Some data have indicated that substantially vertical fractures may be created in some reservoirs. It is believed that the fractures are possibly unsymmetrical, that is, one fracture may extend due north 100 ft and a second fracture on the opposite side of the well may extend south or southeast only 50 ft. The total fracture length, ratios of the lengths and angles of separation may vary considerably. For this reason variations in these factors were considered. The study was restricted to the case of two vertical fractures originating at the well and extending out into the reservoir. It is not known that such will occur in a reservoir, but the results may be of value in interpreting or studying fracturing applications. PROCEDURE An electrical model was used in this study of the effect of unsymmetrical vertical fractures on production capacity, A wooden tank 30 in. in diameter and approximately 2 in deep was coated with paraffin wax. A copper band was situated at the periphery and a single wire electrode was positioned at the center of the tank. The ratio of the reservoir radius divided by the

Jan 1, 1956

By I. Sheinhartz, H. M. McCullough

DURING the course of a lubrication study in relation to the compacting of metal powders, it became desirable to measure the thickness of sprayed graphite coatings on steel dies for hot pressing. The thickness of these lubricant coatings ranged between 0.0001 and 0.002 in. In their particular case, the authors were interested in a method for measuring the lubricant thickness on tapered die inserts having curved surfaces. The lubricant was sprayed on the inserts at an elevated temperature and it was desirable to measure the thickness as soon as possible after application. Various standard types of commercial equipment were tried. Most of the available devices operated on either a mechanical or magnetic principle. The mechanical devices, such as micrometers, dial indi-

Jan 1, 1956