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By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By J. J. Gilman

RECENT experiments have shown that the mar-tensite reaction in a standard tool steel is influenced by the history of the reacting austenite. The martensite reaction proceeds to a given extent at a higher temperature in austenite formed from an annealed spheroidal structure than it does in austenite formed from tempered martensite: that is to say, a prequench lowers the temperature range of the martensite reaction in this steel. Furthermore, a prequench alters the appearance of the martensite as compared to martensite formed from "virgin" austenite. The steel used for this work was a manganese nondeforming tool steel of the following composition: C, 0.85 pct; Mn, 1.43; Si, 0.23; Ni, 0.12; Cr, 0.59; and W, 0.59. A piece from a rolled bar was forged to Vz in. sq and annealed to a spheroidal structure. Disks 1/8 in. thick were used in the experiments. Several sets of the specimens were prepared and austenitized in lead at 1475°F. Three sets were held at 1475°F for 15 min, quenched in water, and immediately reheated to 1475°F. After this quench the three sets were held for 5 min, 30 min, and 3 hr, respectively, at 1475°F and then the individual specimens in each set were quenched in molten baths to 325", 300°, and 275ºF, respectively, and held for 15 sec. Immediately after the quenching treatments? the specimens were tempered at 600°F for 30 sec to darken the martensite and then were quenched in water. The holding times were short enough to avoid isothermal transformation. Three other sets of specimens were given the same final quenching treatments as the first three, but they were austenitized at 1475°F for 20 min, 35 min, and 3 hr and 15 min, respectively, without an intermediate water quench. The two individual specimens from each set were quenched together in order to eliminate quenching errors. Several experiments were run in this way but only the six sets referred to are described in detail because they all yielded essentially the same results. By means of the stated heat treatments the martensite reaction was investigated for: 1—austenite formed from an annealed structure, and 2— austenite formed from tempered martensite. The martensite reactions of the two types of austenite differed significantly. This is shown by Figs. 1 and 2. Comparison of the photographs on the left in Figs. 1 and 2 with those on the right shows that less martensite was formed by a quench to a given temperature from prequenched austenite than from austenite formed from an annealed structure, that is, the prequench suppressed the martensite reaction. The effect was observed for specimens austenitized 20 min, 35 min, and 3 hr and 15 min. A comparison of Figs. 1 and 2 shows that the martensite reactions in both sets of specimens occurred at lower temperatures with increased austenitization time. This was caused by the increased dissolution of residual carbides with time at 1475°F. However, the difference in amount of martensite formed in prequenched austenite as compared to virgin austenite was approximately the same for all three austenitization times. One further observation should be noted. The needles of the martensite formed from virgin austenite are somewhat longer on the average and show less of a tendency to cluster than those of martensite formed from prequenched austenite. This causes the martensite on the right in Figs. 1 and 2 to have a more acicular appearance than the martensite on the left. Since the sets of specimens used in this work were austenitized for identical total lengths of time and the effect of a prequench on the martensite reaction existed for specimens held at the austenitizing tem-

Jan 1, 1953

By Harry M. Bendler, W. A. Wood

Electron metallography has been applied to the study of the torsional fatigue of polycrystalline OFHC* copper. The development of slip bands, fis- sures, and microcracks has been followed as a function of strain amplitude and number of cycles. Those factors that have been found to be relevant to a geometrical theory of the fatigue process are described. From the point of view of this theory it is important to distinguish between the effects of cycling at large amplitudes and at small amplitudes (true fatigue deformation). EARLY investigations showed metal fatigue cracking is caused by continued reversal of a small plastic strain. Fundamental study of fatigue, therefore, has been largely concerned with the cumulative effects of these plastic reversals on the metal structure. In particular, recent work has shown that the plastic reversals produce slip movements that are finer than the slip movements produced by unidirectional increments of plastic strain; individual slip movements in fatigue, for instance, are too fine to see by optical microscopy.2 It has also been shown that the fine slip movements of fatigue tend to concentrate in bands and that in this way they can build up, after enough cycles, a progressive surface disturbance. It is this disturbance which, in effect, makes the slip movement visible. It is also in this disturbance that the first cracks appear to form. From this point of view, therefore, the problem of fatigue becomes one of finding why the fine slip movements should concentrate in bands and why the. bands should finally open into cracks. Thus far, study of the slip bands has been limited to the changes they produce at the surface only. These studies have given interesting results. Ewing and Humfrey3 many years ago showed that the bands in iron could extrude debris. Forsyth found that bands in aluminum alloys could extrude thin tongues of material. Thompson showed that, after lightly dissolving away the surface of copper specimens, some bands persisted as superficial cracks might, and that the life of a specimen under fatigue deformation might be prolonged by dissolving away the surface at intervals. Thus these and related results have suggested that the metal structure in fatigue bands may disintegrate and that this may happen long before obvious cracking. These surface studies, however, have not shown definitely how cracking may begin, for they do not show sufficiently what is happening in depth. However, some advance in this direction has been made recently by a new approach, summarized later, which reveals slip bands and their surface disturbances in section. In the work done thus far, the sections have been studied by optical microscopy only. In the present work they have also been studied by electron microscopy with extended results. This paper also describes some observations on the surface disturbances prior to sectioning. These observations are relevant to a suggested theory of fatigue cracking. REVERSED SLIP MOVEMENTS Slip movements in fatigue deformation must reverse direction in each cycle. The question arises: DO the "backward" and "forward" movements take

Jan 1, 1962

By Donald D. Carr, Lawrence F. Rooney

Perhaps no other mineral commodity in this volume has as many uses as limestone and dolomite. These carbonate rocks are the basic building blocks of the construction industry, the material from which aggregate, cement, lime, and building stone are made. Carbonate rocks, and their derived products, are used as fluxes, glass raw material, refractories, fillers, abrasives, soil conditioners, ingredients in a host of chemical processes, and much more. Although the use of limestone and dolomite goes back before recorded history, new uses and products are continually being found. Carbonate rocks form about 15% of the earth's sedimentary crust and are widely available for exploitation. Found extensively on all continents, they are quarried and mined from formations that range in age from Precambrian to Recent. Reserves of carbonate rock are large and will last indefinitely, although high-purity deposits may be absent or have limited availability in certain areas. Limestone and dolomite are so useful and so abundant that in 1981 about 644 million tons were produced in the United States. In fact, about 75% of all stone quarried or mined in the United States was carbonate rock. Sand and gravel was the only mineral commodity produced in greater quantity. In this chapter we have sought to provide the general reader an overview of carbonate rocks, their composition, distribution, production, and uses, with emphasis on developments since 1960. In doing so we borrowed extensively from our report on the applied geology of limestone and dolomite (Rooney and Carr, 1971). The literature on the limestone and dolomite resources of the United States and Canada is so vast and diverse that one can easily become mired down in print. We tried to list those references that are easily accessible and that provide the economic geologist with a starting point for more intensive study. The table listing selected references on limestone and dolomite resources in Canada and the United States reflects our attempt to be selective rather than exhaustive and to direct the reader to the best sources of detailed information. Geology Mineralogy The principal carbonate rocks used by industry are limestone and dolomite. Limestones are sedimentary rocks composed mostly of the mineral calcite (CaCO3) and dolomites are sedimentary rocks composed mostly of the mineral dolomite (CaCO3 • MgCO3). Aragonite (CaCO3), which has the same chemical composition as calcite but a different crystal structure, is economically important only in modern deposits, such as oyster shells and oolites. Aragonite is metastable and alters to calcite in time. Some other carbonate minerals, notably siderite (FeCO3), ankerite (Ca2MgFe (CO3)4), and magnesite (MgCO3), are commonly found associated with limestones and dolomites but generally in minor amounts. Because of their similar physical properties, the carbonate minerals are not easily distinguished one from the other. Specific gravity,

Jan 1, 1983

By N. H. Fisher

Geographical Distribution 'he most important known deposits in Australia of what are commonly referred to as the beach-sand minerals are along the most easterly part of the Australian coast, between Southport, 17 miles north of the Queensland-New South Wales border, and Ballina, 50 miles south of the border, and most of the production has come from this area (Fig I). Smaller deposits are known to occur farther to the south at intervals for several hundred miles, and beaches have been worked at Yamba, 96 miles south and Woolgoolga, 150 miles south of the border and at Swansea, 60 miles north of Sydney. Important deposits have been shown to exist on north Stradbroke Island and others have been located farther to the north, as far as Tin Can Bay at the south end of Frazer Island. (Fig 2). Table I gives the list of operators with the location of their deposits and workings, their approximate maximum monthly capacity expressed in tons of heavy mineral produced by their concentrating plants before separation into individual mineral concentrates, their methods of mining and concentrating the minerals, and the products obtained. This table applies as of June 1948, but all the operators are remodeling or improving their plants and plant practices will be modified accordingly. In addition, active boring campaigns have been carried out by Alluvial Gold, Ltd., of Sydney, in the Cudgen-Cudgera area, and by Zinc Corporation Ltd., of Melbourne, on Stradbroke Island, and in other places. Physiography Submergence of the order of 100 to 200 ft at the close of the Pleistocene period left the pre-existing hills as promontories and the valleys as deep inlets. Wave action has built bay-bars and sandspits in a northerly direction from the headlands, and lakes and marshes have formed between these bars and the initial post-submergence coast line. These lakes and swamps have been or are being filled in by river-borne sediments or wind-blown sand. Beasley1 has presented evidence that suggests a recent emergence of the coast line of about 10 ft. The evidence for this belief is the presence of a black sand seam 1/3 mile inland and 17 ft above sea level (Fig 3), and although it is not entirely certain that this seam is of beach formation and owes nothing to windblown concentration, other evidence supports the suggestion of recent emergence. Such emergence would undoubtedly aid the formation of bars and sandspits and the easterly progress of the beach front, leaving a series of parallel dunes (Fig 4). This belt of north-south coastal dunes ranges up to 56 mile in width and as many as 15 lines of dune have been counted (Fig 3). The foredune is generally the highest, upto 25 ft high, and there is in many places a flat platform in front of the dune known as the berm. The dunes behind the foredune are lower and less well defined

Jan 1, 1949

By E. A. Gulbransen, W. S. Wysong

The behavior of tungsten and its surface oxides in oxidizing and reducing atmospheres and in high vacua at elevated temperatures is a question of considerable technical importance. The use of tungsten as a a Or as an important component in alloys in high temperature Oxidizing atmospheres has been limited because of the unprotective nature of its oxide film and the volatility of its oxide. This paper will present results of a micro-balance study of the following problems: (1) the oxidation behavior in the ternperature range of 25 to 550°C (') the reduction with pure hydrogen Of thin Oxide films formed On tungsten, and (3) the volatility Of thin Oxide films On tungsten. Tungsten is an interesting metal to study for the following reasons: (1) although the Oxide to to ratio is greater than one, the oxide is not considered protective, ('1 the meta1 readily Oxidizes at temperatures from 30" to 55o°C (3) the oxides WO² and WO³ are reduced at temperatures as low as 500°C. by hydrogen, and (4) the Oxide WO3 is volatile at temperatures from 800 to 1100°C. Literature The oxidation of tungsten in its thin film range has not been studied critically. In the thick film range Dunn3 has made the only systematic study. He found the oxidation rate to obey the parabolic rate law in the temperature range of 700 to 900°c. The temperature variation of the oxidation rate constant was found to follow an exponential law of the Arrhenius type. An inflection was noticed in the temperature plot of the rate law constant at 850 to 900°C. This was attributed to a phase change in the oxides, Schei14 has studied the oxidation rate at 500 and 700°C over long periods of time and found a linear rate law. This result was interpreted as evidence for the presence of a nonprotective film. Pilling and Bed-worth's5 analyses of the oxide volume to metal volume ratio would indicate that a compact protective film should form. McAdam and Geil6 have studied the oxidation of tungsten in the thin film range using the interference color method. A parabolic rate law was found. Their curves showed that tungsten oxidizes faster than nickel but more slowly than iron. The lattice structures found in the oxidation of tungsten surfaces have been studied by Hickman and Gulbransen.? They have reported that WO3 is the stable oxide in contact with the metallic substrate up to approximately 600°C while wo³ forms first at 7oo°c. Hagg and Magneli8 have recently reported a study of the lattice structures . observed in the tungsten oxidcs using the X-ray diffraction method. In addition to an a-phase WO3 and a '-phase WO2, they reported the existence of two new phases. A 8' phase, homogeneous between

Jan 1, 1949

By John Wulff

IN a previous paper Burwell and Wulff1 have shown by electron diffraction studies that allotropic transformations can be induced in 18-8 stainless steel by polishing to a depth of about 5 X 10-5 cm. The development of a successful etching technique, which removes accountable amounts of metal from the surface without pitting and without changing the root-mean-square profile as measured with an Abbot profilometer, led to the application of the whole technique and material to an investigation of various mechanical methods of surface preparation, such as grinding, lapping, superfinishing and cold-rolling. Ideally suited to such a study is 18-8 of low carbon and nitrogen content. The material can be heat-treated to produce a coarse-grained single-phase structure. On cold deformation there occurs not only a reduction in grain size but, at regions of maximum stress, a change of face-centered material to body-centered material, provided the metal is worked below about 200°C. When worked between 200° and 415°C., diffraction studies evidence a reduction in grain size without the appearance of any new body-centered ferrite. Ferrite, which can be referred also to strains induced by carbide precipitation, is evident when the material is worked at temperatures between 415° and 800°C. Stainless steel is advantageous because the usual surface-finishing operations do not readily oxidize it to any appreciable depth. In order to produce detectable oxide films on the surface of austenitic 18-8 in a time equivalent to that required to produce, for example, a fine ground finish on ½ sq. in., the sample must be held in a furnace or oxygen stream above 600°C. By using longer heating times, it is possible to achieve measurable oxide films on samples whose surface temperatures exceed only about 250°C. EXPERIMENTAL PROCEDURE The apparatus, material, and technique described in the previous paper1 were employed in this investigation. Samples of 18-8, 1 by 1 cm. by 4 mm., were carefully annealed in the austenitic range to produce a coarse-grained structure. They were then quenched and pickled to remove scale. On a lapping machine of the Graton2 type, both sides of each sample were polished to a flatness of 1/6 a wave length of sodium D light. Thereafter they were electrolytically etched to remove at least 1 X 10-3 cm. of the surface, a depth that is well below that of any deformations induced by surface preparation. Samples of this material, carefully mounted in steel holders, were then sent to various industrial organizations known for special finishing techniques. In the instrument shops at the Massachusetts Institute of Technology check samples were finished by the same methods, as far as they were available. Abbot profilometer3 readings were made on all the samples, which were then carefully degreased in double distilled benzine and alcohol, dried in a hot-filtered air blast, and kept in a desiccator. Suc-

Jan 1, 1941

By J. F. K. Brown

ANTHRACITE in 1943, in common with the coal industry as a whole, passed through a year of wage negotiations that seemed endless. In the early months discussion of the United Mine Workers' demands was taken up and carried on continuously until May, finally reaching an impasse when the Union refused to continue at work, while submitting their demands to the War Labor Board. Thus a strike threatened, averted by the Federal Government taking over the industry, effective May 1, by order of the President. An office of the Bureau of Mines was established in Wilkes-Barre under the direction of J. J. Forbes, Mineral Production Security Division, as regional manager, who conducted operations until September, 1943, when the collieries were turned back to the operators. But the miners did not agree with the War Labor Board's award rendered in the fall, resulting in a recurrence of the previously threatened strike. again averted by Government control. In addition to the major upsets, a number of individual suspensions occurred at various mines. In spite of these drawbacks, to which might be added the difficulty of obtaining equipment and the scarcity of man power, the industry by November was only little less than a million tons short of the previous year. and in all probability, finally produced but little less than in 1942. This little less. however, was greatly missed in the market.

Jan 1, 1944

By A. E. Back, W. Wyman, K. E. Tame, S. F. Ravitz

In 1940, when it appeared that the United States soon might be cut off from foreign sources of high-grade manganese ore, the Bureau of Mines began an extensive series of investigations on the production of ferro-grade products from low-grade domestic ores by ore-dressing, pyrometal-lurgical, and hydrometallurgical methods. Among the hydrometallurgical processes for oxide ores investigated was a sulphur dioxide process in which the manganese was recovered from solution by precipitation with lime;' this process is essentially as follows: The ground ore is suspended in water and leached with SO2 gas to extract the manganese as manganese sulphate. Calcium chloride is then added to the slurry to precipitate calcium sulphate and form manganous chloride solution, and the resultant slurry is filtered to remove the calcium sulphate together with the insoluble portion of the ore. Calcium hydroxide is added to the filtrate and the mixture is agitated with air to precipitate hydrated oxides of manganese and regenerate calcium chloride. The precipitate is calcined, and the calcium chloride is recycled. To determine manganese extraction, reagent consumption, grade of product, and similar data for this process, a labora- tory investigation was started. Two minor modifications in the process were soon made: (I) the ore was suspended in calcium chloride solution instead of in water in order to extract the manganese and precipitate the calcium sulphate in one step, and (2) the agitation with air after the addition of slaked lime to the filtrate was omitted because manganese hydroxide is readily precipitated without air agitation and can be nodulized or sintered to a satisfactory product. When the process was carried through a series of cyclic tests, it was noted that the concentration of dithionate ion (which is one of the products of oxidation of SO2 by MnO2) in the cycled solution gradually increased; at the same time the chloride content of the solution gradually decreased, owing to soluble losses in the leach residue and in the precipitate. After a number of cycles, the calcium chloride became virtually completely replaced by calcium dithionate, the quantity of dithionate ion formed during the leach being more than enough to make up for the losses of dithionate in filtering. The calcium chloride process thus developed into a calcium dithionate process. Since the latter eliminated the need for make-up calcium chloride, and the dithionate solutions appeared much less corrosive than the chloride solutions, work on the calcium chloride process was dropped in favor of the calcium dithionate process. Acknowledgments The dithionate process was developed by the Bureau of Mines as part of a

Jan 1, 1949

By Harold E. Thomas, Samuel S. M. Chan, Nicholas Bada

The U.S. Bureau of Mines has developed a technique for locating and evaluating bedding plane cracks in mine roof by an air-injection and hot-film flow logging technique. It is ultrasensitive to cracks and is especially useful for detecting the early stage of crack development. Potential applications include: (1) correlation with roof sag measurements, (2) locating cracks for grouting, (3) comparison of mechanical and resin roof bolt effectiveness, and (4) possible delineation of the fracture zone to confirm the arch hypothesis. The required equipment is inexpensive and simple to operate.

Jan 1, 1975

By S. Andrew Kulin, L. Kaufman

A general treatment of the broadening of X-ray double-crystal spectrometer rocking curves due to distributions of tilts and strains has been carried out. The results of this treatment have been applied to the case where dislocations in a crystal give rise to both tilts and strains. On this basis it is found that the rocking-curve halfwidth due to imperfections in the crystal, ßC , increases with increasing Bragg angle, 8. These considerations predict linear relationships between & and tan2 , and ßCand tan 8, for Gaussian and Cauchy distributions of dislocations, respectively. The zero intercept of the ßC us 8 curve, which is a measure of the degree of imperfection of the crystal, is found to depend directly on the distribution rather than the number of dislocations. In addition, the slope-intercept ratio for the ßc - ? curve has been calculated for both the Gaussian and Cauchy distributions. Experimental determination of the - 8 curves for a series of copper single crystals prepared by the Bridgeman and Czochralski methods yields results in agreement with the calculated slope-intercept ratio for a Cauchy distribution of dislocations. CERTAIN X-ray techniques have been used to study the perfection of single crystals. Gay, Hirsch, and Kelly have considered the spreading of spots into arcs on Debye-Sherrer rings due to imperfections. The Double-Crystal Spectrometer has also been applied to this problem.2 The characteristics of Double-Crystal Spectrometer Rocking Curves have been described in the literature by various workers.2-4 By assuming a random spacing of dislocations which give rise to a Gaussian distribution of misorientations relative to some mean orientation in a crystal Gay, et al.,1 arrive at the conclu- sion that the most probable misorientation is given by where h is the spacing between dislocations, and 8 and are the relative misorientations of neighboring regions. If ßC is the halfwidth of the rocking curve (the width at one-half the peak intensity) due to dislocations in the crystal then5

Jan 1, 1960

By Peter G. Groer

Several methods1-3 are being used to determine the WL and individual Rn-daughter concentrations in uranium mine atmospheres. The best of these methods is the one given in Ref. 3. According to this method, the WL and the Rn-daughter concentrations are determined from the total a-counts observed during three consecutive time intervals. Its only disadvantage lies in the fact that rather involved calculations are necessary to convert the observed counts into WL or pCi/l (picocuries per liter). There are, however, counting intervals that give simple weighting coefficients for the observed counts. This fact makes it possible to convert from a-counts to WL or pCi/l with the aid of a graph. After some trial runs on a computer the following equations emerged as the basis for the most practical procedure: [ ] NA, N.., and & stand for the number of RaA, RaB, and RaC atoms per liter of air. C(t1,t2) denotes the counts observed from time t. to time t2 (in minutes) after the end of the 5-min sampling period. E is the detector efficiency and V is the flow rate in liters per minute. With an accuracy loss of less than -5% one finds from [Eq. 1] by adding the corresponding terms: If the WL would have been calculated according to [Eq. 2] instead of using the graph, the result would have been 0.31. Since the values used for C's under [Eq. 3] represent the exact number of counts from a Rn-daughter mixture in equilibrium with 100/3 pCi of Rn the exact WL of this mixture can be calculated easily. The exact value is: [ ] This shows that the method is quite accurate for the 0.3 WL domain. The precision of the method excluding errors made in reading the graph can be estimated with the help of the following formula: [ ]

Jan 1, 1974

By B. K. Larkin

Solutions to the diffusion equation for a line source located anywhere in a region bounded by a circular discontinuity are presented. Such solutions follow automatically from the Green&apos;s function presented by Jaeger.4 Petroleum industry applications of this problem would include transient compressible fluid flow in porous media bounded by a discontinuity. Since several recent papers have treated the subject in less general form, it would appear that many workers in this area of the petroleum industry are not aware of Jaeger&apos;s work. STATEMENT OF THE PROBLEM In several trearments1,2,3 of the transient flow of compressible fluids in porous media it was convenient to consider a region to be bounded by a circular discontinuity. In such a region (Fig. I), the properties in Region 1, r < a, are constant but different from the properties in Region 2, r > a. Hurst, l using the Laplace transform, obtained solutions for a line source located in the center of such a porous medium. The purpose of this work is to point out that a much earlier paper by Jaeger4 presents the solution for a line source located anywhere inside the discontinuity. The assumption is made that a line source may be used to approximate a well. In the following material it is convenient to use the terms source and well as being equivalent; however, the reader should remember the distinction in applications. SOLUTIONS Jaeger presented the Green&apos;s function for a line source, or well, in the composite region shown in Fig. 1. In the most general form, the solution for a system of j wells in Region 1, each producing at a time varying rate, qi (t), is

By Nathaniel Herz

The formula very frequently used for computing the economical size of pipe to transmit compressed air is that of D&apos;Arey, as follows: D = cV w1l Where, D = the volume of compressed air delivered in cubic feet per minute, at the final pressure. c = an experimental coefficient determined for the various sizes of pipe, d = the diameter of the pipe in inches. 1 = the length of the pipe in feet. p, = the initial gauge-pressure in pounds per square inch, p2 = the final gauge-preesure in pounds per square inch. w1 = the density of the air, or the weight in pounds per cubic foot at the initial pressure, p1. The most common case is that in which the given quantities are: the quantity of air required, the length of the pipe, and the initial pressure. The method of solution is to assume a pressure-loss and to compute the remaining factor, cd5, thus giving the size of pipe corresponding to the assumed loss of pressure. It is always desirable to try two or more pressure-drops, in order to find the combination that is most satisfactory, since often a small change in the size of pipe will reduce or increase the loss of pressure several pounds. An alternative method is to assume a size of pipe and calculate the corresponding pressure-drop. Each method involves a series of tedious calculations to arrive at the most economical solution, and also requires the use of tables giving the constant, c, the density of the air, w1, and often, for convenience, a table giving the values of the expressions p1-p2 and c J I hare constructed a graphic chart, Fig. 1, for the solution of

Jan 1, 1913

By N. K. Chen, R. Maddin, R. B. Pond

A METHOD has been described by Andrade&apos; for obtaining very rapid grain growth so that single crystals of high melting point metals could be made with comparative ease. The furnace construction was essentially a very thin wire through which was passed an electrical current so that "a high uniform temperature" was maintained. The wire was surrounded by a fused quartz tube from which the air had been evacuated. Andrade applied this method to the growth of single-crystal wires of alpha iron, and Tsien and Chow2 prepared single crystals of molybdenum 0.25 mm diam in this way. In the present report a method is described in which the basic idea of the Andrade furnace is utilized. However, modifications are employed so that large single crystals of molybdenum or of any refractory metals can be grown. Furnace The modified Andrade furnace is shown in Fig. 1, and the detailed drawing of its construction can be seen in Fig. 2. The furnace proper consists of a 2&apos;/2-in. diam fused silica tube, 20 in. long, which is evacuated continuously at the bottom. Two water-cooled copper electrodes hold the specimen by means of collets held in place in the electrodes by set screws. These electrodes serve also to transmit power to the specimen. The lower electrodes can be clamped to the stand, while the upper electrode is fastened in place to the bellows which in turn is further connected to one side of the lever arm, flexibly supported at the top. After the specimen is mo;nted- and the vacuum is secured, the lever arm is adjusted by means of the counter weight so

Jan 1, 1952

By O. A. Knight

THE suppression of the austenite-martensite transformation that can be brought about by the addition of certain alloying elements, such as manganese or nickel, to plain carbon steel has been known for a long time, especially since Guillet&apos;s investigation at the beginning of this century. The extent to which the critical range is lowered depends upon the percentage and nature of the special element added. First the Ar1 point is lowered gradually, then at a certain percentage a sudden lowering to about 300° C. occurs. The addition of still larger percentages of the alloy may result in lowering the Ar1 point to room temperature or below, in which case the steel remains austenitic at room temperature, especially after rapid cooling. The effect of alloying elements of this general type on the lowering of the transformation temperature is well illustrated by Sauveur(1)§ in his Fig. 281a, reproduced here as Fig. 1. This type of curve is characteristic of both manganese and nickel though it requires about 2 1/2 times as much nickel as of manganese to produce the same result. The influence of nickel in retarding the transformation of austenite into the lower transition constituents is due to its lowering of the critical range of the steel, which is also well illustrated by Sauveur(1) (after Osmond) in his Fig. 284, reproduced here as Fig. 2. Scott(15) presents a diagram illustrating the effect of manganese on the Ac3 and Ar3 points which is strikingly similar to the diagram above referred to in Fig. 2 concerning the effect of nickel.

Jan 1, 1934

By M. R. Tek, F. H. Poettmann, M. L. Grove

The general problem of single-phase natural gas flow through porous media has been considered both by mathematical analysis and field experiments. Theoretical studies on the fluid dynamics of natural gas wells resulted in derivations of expressions which permit a ber-ter understanding of the flow mechanism for conditions under which Darcy&apos;s law is no longer valid. In applying these results to natural gas production and testing technology, special emphasis war placed on the study of low permeability, slowly stabilizing formations. These applications resulted in a method of predicting the performance coefficients of tight natural gas wells. The calculation of the performance coefficient requires the determination of the "test-index", pkh/µ, the drain- age radius, R, and the effective wellbore radius, rw. Methods for estimating these parameters from field data were also developed. Field data from 15 wells were collected and analyzed. The measured values of the performance coefficients were compared with the predicted values. This statistical evaluation gave a bias of 7.14 per cent and a standard deviation of 11.6 per cent. INTRODUCTION The performance of a natural gas well is determined by the physical properties of the reservoir rock, the extent and the geometry of the drainage area, the properties of the flowing fluid, and the conditions of pressure distribution within the drainage matrix. The relation between the quantity of gas delivered and the pressure drop within the reservoir is characteristic of the behavior of each well and is often referred to as the back-pressure behavior of the well. It is well established that for normal, single-phase gas wells the relationship between the gas delivery rates and the bottom-hole pressure take, in general, the form, Q = c(P3 8 -P2 1)n. ,.......(1) where C is the performance coefficient, and n is the exponent corresponding to the slope of the straight-line relationship between Q and (P2 s, — P2 l) plotted on logarithmic coordinates. The determination of a well&apos;s performance by the back-pressure behavior not only permits the production engineers to analyze many operating problems, but also provides necessary information useful and essential to predict the future development of the field.&apos; Important engineering and production problems such as calculation of gas deliverability into a pipeline at a predetermined line pressure, design and analysis of gas-gathering lines, determinations of spacing and number of wells to be drilled during field development to meet future market or contract obligations, etc., all depend, at least in part, on the availability and use of reliable back-pressure curves.&apos; In the past the behavior of gas wells was evaluated

Jan 1, 1958

By H. D. Colson, Robert A. Rapp

When a binary alloy is oxidized to form simultaneously an internal oxidation zone and an external scale which grows at a constant rate, the oxidation should reach a condition of steady shale, in which the internal oxidation zone is maintained at a time-independent thickness. Assuming an ideal model for the steady-state oxidation, the diffusion equation is solved for the steudy-state concentration profiles for oxygen and alloying- element in the metal. A theoretical prediction of&apos; the steady-state thickness of the internal oxidation zone is made in terms of the experimental parameters. FOR the oxidation of binary alloys, Rhines, Johnson, and Anderson,1 as well as Mask: have derived equations describing the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which was assumed to mow according to a parabolic rate law. Experimental determinations of internal oxidation zone thicknesses beneath a Cu2O scale for Cu-Be and Cu-A1 alloys3,4 have shown some deviation from Maak&apos;s theoretical expressions, because the ideal model assumed for the calculation is not met experimentally. Some pure metals, such as columbium and tantalum oxidize at elevated temperatures and high oxygen pressures to form nonprotec-tive external scales which thicken at a constant rate. If such a base metal is alloyed with a solute element which may form a more stable oxide than the solvent oxide, then internal oxidation of solute may occur beneath the growing external scale. A review of the internal oxidation of alloys has been published recently.5 The purpose of this paper is to analyze theoretically for a binary alloy the kinetics for the simultaneous formation of an internal oxidation zone and an external scale which grows at a constant rate. Consider an alloy A-B in which A is the more-noble solvent and B is the less-noble solute. The solute oxide is assumed to precipitate in internal oxidation as stoichiometric particles of BO, which are assumed to have a negligible solubility product in the A matrix. It is further assumed that the diffusion of oxygen through the zone of internal oxidation is not impeded by previously precipitated BO, particles. The specimen is assumed to be sufficiently thick so that the solute content in the center of the specimen does not change. For consistency: the following notation of Maak2 has been used:

Jan 1, 1967

By J. Lohrenz, R. J. Francis, G. C. Clark

Compositional material balance methods have been extended to solution gas-gas cap-water drive reservoirs. Partial or complete pressure maintenance as well as reservoir repressuring by gas and/or water injection may be considered. Increrments of reservoir withdrawals and injections equivalent to a given time increment are used as the basic iterative step to allow the extension. An example field study shows how the reservoir volumes. extent of the water drive, and relative permeability ratio function may be estimated. Knowing these, the methods can be used to predict reservoir behavior. INTRODUCTION The compositional material balance is similar to conventional material balances in many aspects. The assumption of a pressure-homogenous reservoir with no transients is common to all conventional material balances1-1 although numerical methods are different. The compositional material balance also contains this assumption. Inclusion of phase equilibria directly in reservoir calculations is the key difference and improvement in the compositional material balance. A continuous account of the compositions of the reservoir fluids and effluents is determined. Calculations of fluid phases and properties can be based on these compositions. Excepting fluid phases and properties determined in this manner, the compositional material balance uses procedures exactly analogous to conventional methods. Brinkman and Weinaug5 and Jacoby and Berry6 have given compositional material balances for simple solution gas drive reservoirs; subsequently Jacoby and Berry&apos; extended their procedure to include pressure maintenance by gas injection at constant reservoir pressure. This paper extends compositional material balance techniques to a more general combination drive reservoir with various types of pressure maintenance operations. The procedure for this extended compositional material balance and an example of its field application are presented. PROCEDURE The numerical calculations of this compositional mate- rial balance are performed on a high-speed digital computer. The most comprehensive case the present compositional material balance program can handle is a solution gas-gas cap-water drive reservoir with (1) water production, (2) water influx, (3) separate or commingled production from the oil and gas zones, (4) any surface processing arrangement including LPG and gasoline production, and (5) gas injection into the gas and/or oil zones." This description of the procedure applies to this most comprehensive case. Appropriate deletions in the procedure can be made for more simple mechanisms. ASSUMPTIONS In common with conventional material balances, the compositional material balance makes the following assumptions: (1) the total reservoir is at a uniform pressure at a given time; (2) the volumetric ratio of gas to liquid withdrawal at reservoir conditions is directly proportional to their mobilities; and (3) instead of assuming a pressure-dependent total gas-oil equilibrium, the cornpbsitional material balance makes a sianificantly different and more rigorous assumption as follows. Thermodynamic equilibrium exists for each component in the liquid-gas mixtures in the reservoir and in surface processing. These three assumptions are fundamental in the compositional material balance procedure. Other assumptions involve arbitrary simplifications of the reservoir mechanisms. This compositional material balance uses the following simplifying assumptions: (1) no bulk mixing occurs between the gas and oil zone; (2) total mixing occurs between any injected gas and the contents of the injection zone; (3) no in situ hydrocarbon liquid is produced from the gas zone; (4) no reservoir gas is retained behind any net bottom-water influx; (5) the residual saturation of hydrocarbon liquid at reservoir conditions behind any net bottom-water influx is constant; and (6) fluids retained behind any net bottom-water influx exert no further influence on the reservoir. These six assumptions are not fundamental. Modifications of the present procedure can be made for different assumptions of the reservoir mechanisms. THE TIME INCREMENT Previous compositional material balances have used a pressure increment for simple solution gas drive reservoirs"" and an increment of injected gas for pressure maintenance.&apos; These increments are suitable for these simple cases. They are, however, inadequate for reservoirs with time dependent drive mechanisms including water drive. A time increment removes this inadequacy and is

Frank H. Probert, A.R.S.M., Morenci, Arizona (communication to the Secretary): The management of mines and the system of bookkeeping employed are subjects of great interest to mine-superintendents, and such papers as that of Mr. Davis callnot fail to attract attention. The Institution of Mining and Metallurgy, London, England, has done much within the last three years to promote discussion on the many systems adopted throughout the mining world; and any papers giving individual experience will benefit that class of men who are charged with the cconomical management of mining properties. It is often said that " a good mine shows a good manager," and more often that mismanagement is the chief cause of poor returns; or, as Mr. A. G. Charleton puts it, in his able paper on " Mining Accounts and Cost-Sheets,"* " accident may, and often

Jan 1, 1902