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By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.' The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod' and of von Rosenberg' are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger's6 concept of the dispersion of velocities. After a very clear description of Scheidegger's theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By L. W. Bahney

FREQUENTLY in using a thermo-electric pyrometer for measuring the temperature of a furnace, a hole is drilled at the back or side of the furnace, through which is introduced the tube containing the thermo-couple. At times the couple is left almost where it drops, for the reason that it soon becomes too hot to be handled easily, and the space at the back or side of the furnace may be so small and uncomfortably hot that an easy and accurate adjustment is nearly impossible. In order to overcome this clumsy and unscientific method of using the thermo-electric pyrometer, I designed an adjustable stand, to hold the clay or quartz tube unclosing the platinum and plati-num-rhodium leads that constitute the couple of the Le Chatelier thermo-electric pyrometer. This stand also allows an easy and rapid adjustment of position to varying heights and angles, as may be desired for special reading. This stand is illustrated in Fig. 1. The couple in the tube might be of better service if the tube were held a little higher above the charge in a roasting-dish, changing the height and angle if desired. The stand, made of 1.5-in, water-pipe and mounted on casters, is heavy enough so it cannot be tipped over easily. It is adjusted to any position, and has a universal clamp which holds the clay or quartz protecting-tube. To avoid disturbing the wires of the couple at the cold junction each time the tube is moved, the cooling-bottle sets in a wire basket so placed that it moves forward or back with the couple. To overcome the necessity of leveling and adjusting a galvanometer at each furnace, a switch-board is used to connect

Jan 1, 1910

By R. S. Dean

THE first attempt to establish an equilibrium diagram of the lead-antimony series was made by Roland-Gosselin1 in 1896. This investigation classified the system as a purely eutectiferous one, with the eutectic at 12.5 per cent. antimony and 228° C. In the next year, Stead2 placed the eutectic temperature at 247° C. The error in temperature made by Roland-Gosselin, however, has been perpetuated in the literature with a remarkable degree of persistency; this value was accepted by Campbell (1902), and Ewen (1910),3 and will be found in the last edition of Desch's3 Metallography (1922). Gonterman's investigation, made in 1907, was the most complete one available at the time the present investigation was started. He concluded' that the system was a simple eutectiferous one and placed the eutectic at 13 per cent. antimony and 247°C. Other investigations by Tammann (1907),5 Garbow (1909),6 Rudolfi (1910),7 Loebe (1911),8 and Leroux (1913)9 added little, if any-thing, to Gonterman's diagram. A number of investigations have been made of physical properties of the alloys. The electrical conductivity of the series was studied by Matthiessen (1860)10 and by A. W. Smith (1921);" the thermoforce by Rudolfi (1910),12 and Pelabon (1923);13 the specific heat by Durrer

Jan 2, 1926

By Lyall Zickrick, R. S. Dean, F. C. Nix

The first attempt to establish an equilibrium diagram of the lead-antimony series was made by Roland-Gosselinl in 1896. This investigation classified the system as a purely eutectiferous one, with the eutectic at 12.5 per cent. antimony and 228" C. In the next year, Stead2 placed the eutectic temperature at 247' C. The error in temperature made by Roland-Gosselin, however, has been perpetuated in the literature with a remarkable degree of persistency; this value was accepted by Campbell (1902), and Ewen (1910),3 and will be found in the last edition of Desch's3 Metallography (1922). Gonterman's investigation, made in 1907, was the most complete one available at the time .the present investigation was started. He concluded4 that the system was a simple eutectiferous one and placed the eutectic at 13 per cent. antimony and 247° C. Other investigations by Tammann (1907),5 Garbow (1909),6 Rudolfi (1910),7 Loebe (1911),8 and Leroux (1913)9 added little, if anything, to Gonterman's diagram. A number of investigations have been made of physical properties of the alloys. The electrical conductivity of the series was studied by Matthiessen (1860)10 and by A. W. Smith (1921);11 the thermoforce by Rudolfi (1910),12 and Pelabon (1923) ;13 the specific heat by Durrer

Jan 1, 1926

By W. D. Robertson, E. G. Grenier, V. F. Nole

The electrical, mechanical, and corrosion cracking properties of an age-hardenable Cu-Ni-Si alloy have been studied over a range of time, temperature, and deformation states for the purpose of determining the relationship between the properties and the structural state. The precifitate has been identi3ed as and the sites of preferred precipitation have been located by electron microscope studies of the structures developed by various combinations of heat treatment and plastic deformation. An extreme form of deformation banding has been observed in the aged alloy that results in high strain concentration in bands lying parallel to {111} planes. These bands are the structural paths along which transcrys-talline cracks propagate in the deformed alloy. The observations provide a basis for a general mechanism of transgranu-lar corrosion cracking of face-centered cubic alloys in terms of stacking fault probability. AMONG the age-hardening copper alloys the copper-nickel-silicon (Silnic Bronze) type is outstanding in exhibiting a high strength combined with a considerable capacity for cold working, a relatively high conductivity, and a low to negligible susceptibility to stress corrosion cracking. It is not a new alloy and it has been the subject of a number of investigations,1-5 which were made primarily to establish practical composition and heat treatment limits. The structural characteristics of the aging processes in this alloy have not previously been studied in detail. This particular investigation was undertaken to explore, in detail, and over a wide range of conditions, the properties obtainable by various combinations of working and heat treatment and to correlate structural changes with the observed mechanical, electrical and corrosion properties. MATERIAL AND PROCESSING Eight different commercial heats of the alloy were made and used in the investigation. The range of composition among the eight heats is shown in Table I. Billets, 8 by 24 in., were cast into water-cooled molds, extruded to 1.687-in. rod, and quenched in water after extrusion. Extruded material was rod rolled to 0.750 in., annealed at 1450° F for 2.5 hr, and quenched in water. Subsequent working operations were performed by tandem rolling to various sizes depending on the degree of reduction required. Final cold-working operations were performed by drawing to a uniform size of 0.187 in. diam and straightening by a roller straightening machine (Lewis). The combinations of heat treatment, working and aging that were investigated are summarized in Table 11; the various treatments were performed in the order given in each row of the table, and they will be subsequently identified by the symbols shown in the first column. SOLUTION TREATMENT All material investigated in the cold-worked condition, or cold worked prior to aging, was solution

Jan 1, 1962

By G. C. Stone

The method of making oxide of zinc direct from the ore was invented and developed at the works of The New Jersey Zinc Co. at Newark in the middle of the last century. The process was invented by Burrows, who had not the ability, financial or technical, to work out the details necessary to make it of commercial value. This was done by Col. Wetherill, whose name is commonly attached to this process. The grate bars used are also frequently called Wetherill grates, which is a misnomer because they were in common use for boiler firing at the time, and he never claimed their invention. The invention of the process was due to the efforts of The New Jersey Zinc Co. to find a profitable means of working the ores from Franklin and Sterling Hill, N. J. These are a mixture of franklinite, willemite, and zincite, containing about 20 per cent. of zinc. The first attempts were to make spelter, which were not successful, owing to the low grade of the ore and the fusibility of the residue. Failing in this, the next attempt was to make oxide in large muffles and reverberatory furnaces. This succeeded, although the cost of operation was high, the recovery low, and the quality of the product uncertain. In 1855, the new process was patented and has been in successful operation ever since. Essentially, the process is to spread a mixture of coal and ore on a body of burning coal on a perforated grate, and blow an excess of air through the grate. The zinc is reduced in contact with the coal, volatilized and burned by the excess of air in the upper part of the furnace and in the flues. It is then carried to the bag rooms by the excess air and products of combustion which are foreed through the flues by fans. In its main features, the process is the same today as at the time of its invention, but the details have been so modified that it would hardly be recognized by its originators. OrEs The process is applicable to all the oxidized ores of zinc and to roasted sulphides, provided the gangue is not so fusible as to leave a residue that is impervious to the blast. In many cases the ores contain impurities that make it impossible to produce an oxide of a good enough color to be

Jan 1, 1918

By Leonard H. Goldman, Harold E. Marr

The PGT uranium assay probe is a borehole tool developed by Princeton Gamma-Tech over the last several years. It has the ability to do an in-situ assay of uranium in the presence of any amount of disequilibrium. It has some advantages over coring including cost, speed of analysis, and accuracy. In this paper we would like to give a brief description of the measurement and then show some sample logs from South Texas. Uranium exploration and development is carried out primarily by gamma logging since uranium daughters are prolific emitters of gamma rays. The conventional gross gamma tool for uranium logging is limited in value because of the inability of this tool to distinguish uranium from its daughters and other naturally occurring radioisotopes, such as potassium and thorium. This problem becomes severe in cases of disequilibrium. Disequilibrium, in a geological context, is defined as the condition when the gamma radiations from the daughter products are being emitted in a location different from that of the parent uranium. In the decay chain of uranium almost all the gamma radiation emitted in the entire chain comes from the daughter product, bismuth-214. Bismuth-214 is separated from uranium by several long-lived isotopes that are chemically active and have different physical properties, often resulting in shifts in the location of bismuth- 214 relative to the parent uranium. In the United States orebodies exhibiting disequilibrium are a common occurrence and the use of a gross gamma log to delineate uranium orebodies can lead to errors. At present the solution to the disequilibrium problem is extensive coring followed by chemical analyses of the cores. There are several drawbacks in using this technique. First is the high cost of coring, the second is the fact that no results are available for days, or typically, weeks after the drilling is done. Thus for development work, coring and drilling must be done on a grid basis and many additional holes are cored to ensure that the entire orebody is mapped. Another disadvantage to cores is the fact that a small volume is sampled, the volume of the core itself. This leads to problems in the mapping out of the orebody when the ore de- posit is not very homogeneous. The PGT probe described in this paper is a new solution to the disequilibrium problem. Basically, the probe measures radiations that come almost directly from uranium itself. The first daughter of uranium, which is protactinium-234 (Pa-234), is only separated from uranium by a 24-day half-life and no disequilibrium problems build up in such a short time. The PGT probe measures the intensity of a one MeV gamma line emitted by Pa-234 and, using this information, calculates the concentration of uranium. The PGT probe is 24" in diameter and 12 feet long. The probe contains a microprocessor which passes the information to a larger minicomputer in the truck. All data is analyzed on site, and the results from a high speed printer are presented to the geologist. Data is also available on 9- track IBM compatible tape for further processing. The PGT probe output is linear with uranium concentration. The only correction factor is for borehole size, and that only becomes important in boreholes bigger than seven inches in diameter. Dead time is compensated in the probe itself and no problems have been encountered in ore zones up to several percent UjO8. In addition to the uranium assay, a conventional gross gamma log is plotted alongside. Grade thicknesses for zones above cutoff are calculated as well as disequilibrium factors. COMPARISONS During its commercial operation PGT logged a series of 18 holes that had been cored and assayed. All of the holes in this series were logged in normal operation by regular field operators. The time to log each hole was generally under an hour, and in typical operation a PGT logging truck will do between 7 and 8 holes a day. The results of the comparison of the PGT and the core assays are presented in a series of figures showing plots of the PGT assay, core analysis and gross gamma measurements. The first three figures show individual holes with the gross gamma plotted along with the core and the PGT assays. All three logs were from holes on the reduced side of a rollfront deposit in South Texas. In Figure 1 we see the two wings of the roll- front at 143 ft and 150 ft separated by a barren zone. The wings are well defined both by the PGT assay and the core. There is approximately a one foot shift which can be attributed to drilling errors. The gross gamma is showing a rather severe discrepancy, being considerably lower and not showing the barren zone. The grade thickness calcula-

Jan 1, 1980

By R. H. Heyer, J. L. Bray, M. E. Carruthers

It is well known that iron markedly improves the physical properties and casting characteristics of aluminum bronzes. The use of 1 to 4 per cent iron as the principal modifying addition has become common practice in many foundries melting aluminum bronzes. Although the beneficial effects of iron are unquestioned, there is some uncertainty regarding the structural changes caused by it in the basic copper-aluminum system. It is agreed that a new constituent appears in abundance when the iron content reaches 2 to 4 per cent. This constituent, which frequently occurs in shapes resembling clover leaves, is sometimes assumed to be an aluminum-iron intermetallic compound. If this were correct we might expect a change in the structural relationships of the matrix in the direction of decreased aluminum content. On the other hand, it has been reported that iron has a negligible effect in altering the fundamental relationships of copper-aluminum alloys1 Others2'3 have reported an additive coefficient. Apparently it will be necessary to know the equilibrium relationships between the phases of the copper-aluminum-iron alloy system to establish any such theory as fact. When this has been done it may very well be that a further revision in the structural relationships may be necessary to describe the changes to be expected in commercial cast alloys. It was with this latter problem before them that the authors attempted to determine the change in the copper-aluminum relations with respect to iron. Objects of the Investigation In certain investigations carried out by the authors for a plant producing a large tonnage of cast aluminum bronzes the structures

Jan 1, 1936

By Gilbert Thiessen

THE purposes of this paper are (1) to show that the mineral matter content of coal is satisfactorily represented by the Parr formula; that is, Mineral matter = 1.08 Ash + 0.55 Total sulfur (2) to compare ash-to-mineral-matter ratios with factors by which ash values must be multiplied in order that dry, factor-times-ash-free values shall equal Parr unit coal values; (3) to examine such ash-correction factors and to compare them with similar factors corresponding to certain simplifications or modifications of the Parr formulas and (4) to show that ash-correction factors used for simplification in calculating approximate unit coal calorific values cannot be. correctly used for the conversion of other determined values in an analysis to the unit coal basis, but that each type of calculation requires separate treatment in simplification.

Jan 1, 1934

By F. H. Newell

In 1888 the United States Geological Survey began a systematic examination of the water-resources of the West, comparable in character and scope to the study of the deposits of ores or coal. As experience was acquired, the surveys were extended to the East, until now they embrace representative localities in all parts of the United States. The object to be attained is to note and record the distribution of water-supply, and to learn, as far as practicable, the laws governing its fluctuations.

Jan 1, 1901

By E. Hornbogen, R. C. Glenn

Copper precipitates from a iron as fcc E phase without formation of intermediate compounds. In the first stage of the precipitation, spherical particles with diameters < 100A are formed at a high rate. During the second stage, the particles grow at a rate given by Zener&apos;s equation for growth of a spherical precipitate. In the third stage, growth is slower. Rod-shaped particles form after long aging times at 700°C. Maximum strengthenzng was observed at the beginning of the second step of precipitation. During plastic deformation of the aggregate, particles appear to deform initially by twinning. THE work discussed herein was part of a study of precipitation of substitutional elements from a iron. Copper was chosen as one of these substitutional elements because it has about the same atomic size as a iron, and does not form an intermetallic compound with iron. The data on the iron-copper system then available were summarized by Daniloff1 several years ago. The solubility of copper in a iron has been determined by electrical conductivity measurements,2 lattice parameter measurements,3 and by saturating thin iron foils with copper and determining the copper content.4 The results of the three investigations do not agree very well, but the value of 2.4 wt pct for the maximum solubility at 840°C seems to be the most reliable,4 Fig. 1. An alloy containing 1.23 wt pct Cu was used in our work to assure starting with a completely homogeneous material. On the copper-rich side of the diagram, there is a maximum solubility of about 4 wt pct Fe in copper at 1094°C ( phase). The precipitation of

Jan 1, 1961

By V. R. Garfias, C. O. Isakson

The production of petroleum in Mexico during 1930 was approximately 39,600,000 bbl., or 5,188,000 bbl. less than in 1929. The decline which has continued for the last eight years, will place Mexico in fifth or sixth rank as an oil-producing country. The production of the northern and southern fields near Tampico declined over 5,250,000 bbl., while that of the fields in the Isthmus of Tehuantepec moderately increased. The wildcat operations which have been conducted for some years near the international border along a 290-mile belt, extending roughly 170 miles northwest and 120 miles southeast from Laredo, Texas, have so far met with little encouragement, although the oil possibilities of the region warrant the belief that commercially productive fields will be discovered eventually. An interesting development during the year was the starting of construction of the oil pipe line from Palma Sola in the South Fields near sea level—over Sierra Madre at 8660 ft.—to Atzcapotzalco, a suburb of Mexico City at an elevation of 7350 ft. This line, about 146 miles long, has a diameter of 10 in. and an estimated daily capacity of 10,000 bbl., and with its terminal refinery at Mexico City will form a transporting and refining unit which should materially affect the distribution and marketing of refined products in the Republic. Development During the past year 148 wells were drilled, as compared with 214 in 1929 and 371 in 1928, the percentage of producers being 49 as against 47 in 1929. With the exception of one well in San Isidro, at the extreme southern end of the Golden Lane, the Jardln Paso Real area was the only sector of the old fields where new development could be considered as successful, all other producers brought in during the year being drilled in nearly exhausted pools to be operated as (&apos;strippers." Northern Fields A total of 71 wells were drilled in the northern fields, of which 22 were producers; one well in Ebano was estimated at 5000 bbl. per day, while the general average of all producers was less than 300 bbl. Results

Jan 1, 1931

By F. B. Plummer

GEOLOGICAL engineering as applied to oil fields, or production geology as some prefer to designate the profession, is designed to fill in the border line between pure geology and pure petroleum engineering. Therefore the production geologist may, and frequently does, reach out to grasp much in both professions. Where once the oil geologist was content to pick samples out of a mud ditch and try to identify oil formations from the color or appearance of flakes of rock bailed out of a well, now he has to deal with graphic electrical logs obtained by intricate and highly technical electrical apparatus and to make exact determinations to the fraction of an inch of the depth and thickness of an oil sand 2 miles below the surface.

Jan 1, 1944

FROM the first to the last meeting of t h e Rocky Mountain Club John Hays Hammond served as president. He guided its deliberations when there were any, but that always y o u n g organization was never particularly deliberate. Youth never is. And the Club was the embodiment of the youthful spirit of the West, which considers any- thing can be done if there be but the will to do it. Ham- mond and the others came out of the West, but they, brought the West with them P and in all the far countries in which he has served his profession and in all the honorable offices in which he has served his country, he lived true to the ideals under which he was raised. A Californian, born in San Francisco in 1855, the son of an army officer, Major Richard Pindell Hammond, educated in the public schools of his native city, at Yale, and at Freiburg, he turned early and quickly to mining. He served his apprenticeship as all successful mining men do, as assayer, surveyor, as assistant in ex-aminations and later as principal, and finally as mine manager. Even in those days of beginnings, his future world-wide career was foreshadowed in that Mexico as well as California served as his training school. His first major step up the ladder was in connection with the Bunker Hill and Sullivan mine, where he served in various positions finishing as president and considerable owner. It was from this great lead mine that he was called to South Africa, where he remained a number of years and was the technical expert who guided the great enterprises of Barnato Brothers and Cecil Rhodes. The story of his activity in developing the "deeps" of the Rand and in opening Rhodesia has been often told but is always an alluring one of adventure and accomplish-ment. After his famous escape from death at Johannes-burg as a member of the Reform Committee, he went first to London and later returned to the United States representing both British and American capital in the purchase and development of great mines in all parts of the world. For some years he was general man-ager, consulting engineer, and director of the Guggen-heim Exploration Co., but of recent years he has oper-ated entirely on his own account and with marked success.

Jan 4, 1928

By C. E. Beecher

THE application of gas or air under pressure to obtain more oil from a sand which has been practically exhausted by ordinary production methods has been practiced to a limited extent for many years. Until recently such methods were confined to the Eastern fields, principally those of Ohio and West Virginia, where in many cases the production obtained after applying pressure for a few years was nearly equal to the total production prior to that time which had been obtained by the usual production methods.&apos; As early as 1917, J. 0. Lewis1 called attention to this method of increasing the recovery of oil and cited the phenomenal results obtained by H. E. Smith, I. L. Dunn and 0. C. Dunn, who pioneered the application of air or gas pressure recovery methods. With this information available it would appear that other oil-producing sections of the country have been extremely slow to realize the advantages of repressuring. However, after a few successful projects in the Mid-Continent area, the oil producers appreciated the value of this method for obtaining further and profitable production from their practically exhausted leases and are now making extensive use of it. In general, it has been the practice to apply pressure to the sands when production has declined to a small yield per well. The purpose of this paper is to discuss some of the advantages which may be expected from returning gas under pressure to the oil sands during the early stages of development, before the rock pressure has been dissipated and the gas exhausted, and to stimulate discussion of this subject on which comparatively little actual field data are available.

Jan 1, 1928

By W. C. Leslie, R. M. Fisher, K. G. Carroll

A nitride, believed to be Si3N, has been separated from three nitrided silicon steels. Germanium nitride, Ge3N4, has been prepared from pure germanium. Comparison of the diffraction patterns indicates that the two nitrides are isomorphous; on orthorhombic structure is suggested in place of the rhombohedral structure previously reported for Ge3N4. THE possibility that a nitride of silicon may, under appropriate conditions, precipitate in silicon steels or in steels killed with silicon makes it desirable to have some positive means of identifying such a compound. One such means is the X-ray or electron diffraction pattern of the nitride. A review of the meager data in the literature indicates that the nitride most likely to form is Si3N4, a conclusion supported by the results of a study of nitrided silicon steels to be published shortly by L. S. Darken and R. P. Smith, of this Laboratory. Unfortunately, there is available no diffraction pattern for this nitride. Data have been reported, however, for Ge3N4 which, judging from the similarity between germanium and silicon, might be expected to be isomorphous with Si3N4. An effort was made, therefore, to form such a silicon nitride, to determine its composition and diffraction pattern and, if possible, its structure. To this end a series of three silicon steels was nitrided under controlled conditions with the resultant formation of nitride particles which yielded an electron diffraction pattern in situ. The particles were then extracted from the steel and an attempt was made to determine their chemical composition. X-ray and electron diffraction patterns were also obtained from the extracted particles, which indicate that the nitride is isomorphous with Ge3N4, although a complete determination of the structure has not been possible. These results show that a silicon nitride with a well-defined diffraction pattern can form in silicon steels, and they suggest that this nitride is Si3N4. Materials and Procedures The sillicon steels investigated were In the form of thin sheet or strip and had the composition shown in Table I. The 0.58 and 1.21 pct Si steels were nitrided by holding them at 1110°F in an H2-NH3 atmosphere containing 3 pct ammonia for 48 hr. The nitride particle size was increased by subsequent heating at 1500°F for 13 1/2 hr in helium. The resulting microstructure is shown in Fig. 1. The steel containing 3.20 pct Si was nitrided at 1200°F for 16 1/2 hr after which it was held in helium at 1500°F for 4 hr. Its structure as seen under the electron microscope is illustrated by Fig. 2. As would be expected from the higher silicon content and the shorter holding time at 1500 °F, the nitride particles are smaller and more numerous than those in the 1.21 pct Si steel. The ammonia-hydrogen treatment reduced the carbon content of the steels to a very low level, so no interference was encountered from carbon or carbides. In the case of the 3.2 pct Si steel, the carbon was reduced to 0.003 pct before nitriding by heating in dry hydrogen. Attempts to obtain an X-ray diffraction pattern from polished and etched surfaces of the 1.21 and the 3.20 pct Si steels were unsuccessful. However, an electron diffraction pattern was obtained from the surface of the steels. The interplanar spacings obtained from these patterns arc shown in Table 11, col. 5. The nitride particles were then extracted from all three steels by dissolving the ferrite matrix in bromine-methyl acetate, the solution used in the Beeghly method for the extraction of aluminum nitride from steel. X-ray diffraction patterns of these residues, obtained by means of a spectrometer and by a 57 mm Debye-Scherrer powder camera using filtered cobalt or chromium radiation, are given in Table II along with the pattern obtained by

Jan 1, 1953

By K. Barron

The glass insert stressmeter, or photoelastic stressmeter, is an instrument designed to determine stress changes occurring in rocks. It has several potential advantages over other such devices in that it is a biaxial device, it is simple and it is cheap to make. The object of this study was to assess the behaviour of the meter under biaxial loads and to examine some of the problems associated with measurement and interpretation of the fringe pattern. This assessment has been carried out by comparing theoretical and laboratory behaviour of the meter. It has been shown that: a) There are certain optimum measuring points in the meter at which measurements should be made for best accuracy. The position of the points depends on the ratio, n, of the biaxial stresses. b) The meter&apos;s sensitivity can be assumed to be independent of the rock modulus E provided that the rock modulus is < 2.5 x 106 psi and not, as previous workers have assumed, if E < 5 x 106 psi. c) There are several methods of separating the principal stresses; some of these are unsatisfactory. A new method is proposed and discussed. d) The meter sensitivity decreases as the ratio of the biaxial stresses approaches unity; the accuracy thus also decreases. e) The axes of symmetry of the fringe pattern give an excellent indication of applied stress direction. f) Laboratory calibrations are in good agreement with theory. The glass insert or photoelastic stressmeter is an instrument designed to determine stress changes occurring in rocks. It has several potential advantages over other such devices in that it is a biaxial device, it is simple and it is cheap to make. This stressmeter has been described in detail.l,2 Basically it is a hollow glass cylinder that has at one end a light source and filters producing circularly polarized light. The glass cylinder and source are grouted into a borehole in rock and the face of the cylinder is viewed through a quarter wave plate and an analyser. If, after installation, a stress change occurs in the rock, then a distinct colored isochro-matic fringe pattern is seen in the meter. The fringe order at any point in the meter can be determined by counting the fringes and measuring the fractional fringe orders by the Tardy compensation method. The relation between the fringe order at any point and the applied stress change can be determined either by calculation or by calibration. The object of this study was to assess the behavior of this stressmeter under biaxial loading conditions and to examine some of the problems of interpretation of the fringe pattern. THEORY Hiramatsu et a14 have determined the stress distribution in a hollow cylindrical inclusion in an elastic host material when subject to uniaxial stress. Using this solution, the biaxial case of stress p in the x direction and stress q in the y direction (Fig. 1) can be solved by superposition. This has been done in Appendix 1. It is shown that the principal stress difference (s1 -s2) at any point (r,?) in the cylinder is given by:

Jan 1, 1965

By J. R. Kyte, L. A. Rapoport

The material balance equation for partiai or complete 1:trter-drivc reser1,oir.s been re-arranged to include a pressure irrferferencr ternr. This pressure interfernce term was ohtained from the theory established hy Morinda. A .successful progranl deissed to solve the resrclritlg c,qrration in a few hours on a nleelitr .sizeti, digital compuier. No prior knowdelge of the properties of the eqrrifer is required in the solution. 7&apos; ri~rl calculations areatle using various assumed con!binuiions of value of the constant expretsing the qquifer properties correspoinds to the best fit ohtained between observed and calculated field history. Details of the method of calculaion are illus trated by an example. INTKCDUCTICN A method 01&apos; calculating the material balance equation for a partial water-drive reservoir completed in an aquifer has been described in the literature." Pressure interference i&apos;rc,m other pools iocated in the same nquiucr is not taken into account in this solution. When present, the pres- sure interference effect must be included in order to make a complete performance analysis. A correction for this effect has been developed using the theory cstahlished by Mor-tada.&apos; Manual calculation of the material balance for water-drive reservoirs is a formidable task. Such manual ca1culation when interference eflects are includcd would be impossible to completc in any reasonable time period. However, a medium-sized stored program, digltal conlputer can he used satisfactorily. The method is described in the following sections. THECKETICAL CONSIDEKATIOhS The material balance equation for a reservoir producing by partial or total water drive, as proposed by Van Everdingen, This relationship is linear for Z/a from which thc slopc, Z, and the intercept, N, can be obtained by the least-squares method from the data points. It is not necessary lo know the aquifer properties to uktain oplimum values tor 2nd IV. Various assumptions are made tor At,,: where 11 is production time, seconds (oilfield between the equal successive time intervals into which the history is divided. t,, h It, times the number of equal time periods from i.e.. the total dimen-sionless time interval from It is noted that the dinlensionless time interval, At,,, involves all the relevant aquifer properties. Accordingly, any assunlption of is an assumption of the combined aquifer properties which pertain to the solution of the equation. Deviations of the data points from a straight line arc calculated for each assumption of and the value of A, correspond ing to the minimunl deviation is chosen as the optimum solution. This method is described in Ref. 1 and 2. Thc material balance solution is usually made with an initial assumption that the reservoir being studied is located in an infinite aquifer from which there are no other withdrawals. Deviation of the points by amounts greater than can be attributed to inaccuracies in field data may be the result of: (1) boundary effects of a limited aquifer, (2) pressure interference from othcr pools completed in the .sarne aquifer, and (3) a combination of these effects. Differentiation of these effects can be made only on the basis of geologic data. Pressure interference from other fields will result in a pressure drop at the original oil-water boundary having an interference component, The measured instantaneous pressure drops at the oil-water

By Rollyn P. Jacobson

The town of Pacific, in Jefferson County, Mo., is 27 miles west of St. Louis. Since the area lies entirely on the flood plain of a cut-off meander of the Meramac River, it was considered a likely environment for accumulation of commercial quantities of sand and gravel. Excellent transportation facilities are afforded by two major railways to St. Louis, and ample water supply for washing and separation is assured by the proximity of the river. As a large washing and separation plant was planned, the property was evaluated in detail to justify the high initial expenditure. An intensive testing program using both geophysical and drilling methods was designed and carried out. The prospect was surveyed topographically and a 200-ft grid staked on which electrical resistivity depth profiles were observed at 130 points. The Wenner 4-electrode configuration and earth resistivity apparatus* were used. In all but a few cases, the electrode spacing, A, was increased in increments of 1% ft to a spread of 30 ft and in increments of 3 ft thereafter.

Jan 2, 1955

By J. H. Bowden

The shaft-plant here described was put in operation in September, 1895, and the No. 6 slope-motor was started in May, 1896. The plant comprises : One Norwalk three-stage compressor l21/2, 91/2 and 5 in. diameters of air- and 20 in. diameter of steam-cylinder, all 24 in. stroke; capacity at 100 revolutions, 296 cu. ft. of free air per minute, compressed to 600 Ibs. per sq. in. A main pipe, 5 in. diameter, 4380 ft. long, with five charging-stations in No. 6 Shaft, and a branch of 3 in. pipe, 3100 ft. long, with three charging stations, in No. 6 Slope. These pipes on each line charge a Porter compressed-air motor, with 7 by 14 in. cylinders, and four 24 in. drivers, weighing about eight tons, with a tank-capacity of 130 cu. ft. of air at 550 lbs. pressure in the main tank, reduced to 160 lbs. in the 8-in. auxiliary tank of 4.2 cu. ft. capacity, supplying the cylinders. The No. 6 shaft run averages 4000 ft. each way on grades of $ to 23/4 per cent., and averaging close to one per cent. in favor of the loaded cars. The No. 6 slope run averages 2100 ft. with nearly the same grades. The mine-cars weigh 2800 Ibs. empty, and about 9800 lbs. loaded, and are hauled in trips of 12 to 20, averaging about 15 cars. The shaft-motor now hauls about 355, and the slope-motor 320 cars per day of 10 hours, replacing in the shaft 17 mules, and

Jan 1, 1901