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By John N. Hobstetter

IT is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spontaneous diffusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow,' Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Becker1 in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r. beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration, The increase in free energy per mole accompanying the formation of a nucleus which is just stable, ?fe, is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. THE NATURE OF THE NUCLEUS It is necessary to have rather detailed knowledge of the nature of a nucleus if ?Fe is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown3

Jan 1, 1948

By J. Chipman, N. J. Grant, R. Rocca

D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—With reference to eqs 7 and 8, at what temperature do they apply John Chipman (authors' reply)—That was 1600°C. Dr. Babcock—You have l x 10-4 as the component for the lime and 1 or 4x10-. Now, is it by dividing one into the other you get the 400? That is assuming equivalent activity on the part of oxygen, sulphur, and magnesia. Dr. Chipman—Yes, they are calculated for 1600. Now, the first one for CaO was calculated before we had a glimpse of Dr. Rosenqvist's paper." If you take his calculation you get 14,000 cal which is very good agreement, but our calculation would be superseded by Dr. Rosenqvist's new data. Dr. Babcock—The state you assume those to be in is the liquid state, as near as you can measure? Dr. Chipman—Naturally it is based on the solid CaS, but if you add the effect of fusion on both sides it just about balances out, so the ratio would be about the same. B. M. Larsen (U. S. Steel Co., Kearny, N. J.)—If we knew the activity of sulphur in the slag instead of merely the percentage, we might be able to find some conflicting factors that balance one another out, and find that the FeO or oxygen pressure effect is really present over the whole range. Dr. Chipman—I am fairly sure we would. The activity of sulphur in the slag and the activity of CaO in the slag, if we just knew those quantities, would enable us to save a lot of this computation and assumption and all the approximations we are doing now. Mr. Larsen—Two other points perhaps should be included: 1—an independent effect of manganese in helping the desulphurization; and 2—the number of mols of constituents or number of mols of ions or whatever there is in the slag could vary with these compositions in such a way that you get dilution effects. Dr. Chipman—You can figure all that in if you want to and it might improve the degree of approximation a little bit. Maybe enough to justify the labor of calculation, inaybe not, but we did not do it. L. S. Darken (U. S. Steel Co., Kearny, N. J.)—The authors have tackled a very complicated problem in trying to tie together in one picture the desulphurizing problem over the wide range of basicity and oxidation level from that of the open hearth to that of the blast furnace. At the present state of our knowledge of slags such an ambitious undertaking necessarily involves the adoption of numerous hypotheses. Their formulation (eq 11) for the higher FeO range

Jan 1, 1952

By P. van Meurs

This paper describes a technique which permits visual observation of oil displacement processes througlrout the interior of a porous structure as thick as 2 in. A model having glass walls is filled with finely powdered glass. Such a model becomes completely transparent if the powdered glass pack is saturated with an oil having the same refractive index as the glass. When water or gar, with a refractive index different from that of the oil (glass) is injected, the model becomes opaque in the space occupied by the water (gar). visual observation and photography of these displacement processes are thus rendered possible. The following processes have been studied: (I) displacement of oil by water (linear drive) in a homo-geneous formation and in a stratified formation, (2) water flooding (five-spot well pattern), (3) solution gas-drive process, and (4) oil-bank formation. INTRODUCTION Most of the scaled model experiments heretofore carried out in the Koninklijke/Shell Laboratorium, Amsterdam, have been done in steel containers, in which oil-saturated sand packs represented the oil-bearing formation. In such experiments, for instance those on the displacement of oil by water, the cumulative oil production was measured as a function of the cumulative water injection. In order to interpret the measured production data, a need has for some time been felt for a means of observing visually what happens in the course of such experiments. Some information of this kind was obtained earlier by observing the water-oil distribution in various cross sections of the sand after the conclusion of the experiment.' However, the technique used did not guarantee that the fluid distribution remained undisturbed. Moreover, the procedure was somewhat elaborate and the information obtained limited. Therefore a new technique has been developed, which is described below. DESCRIPTION OF EXPERIMENTAL TECHNIQUE AND APPARATUS Glass models simulating part of an oil reservoir are filled with ground Pyrex glass of a specific grain size, representing the porous structure of the prototype. Before an experiment is started, the porous formation has to be saturated completely with an oil having exactly the same refractive index as the Pyrex glass powder. All light-scattering surfaces of the glass grains become invisible and the formation is then transparent. If the oil is displaced by another fluid (e.g. by water in a water-drive experiment, or by gas liberated from the oil in a solution gas-drive experiment) the formation becomes opaque in the region where the oil is expelled from the rock.* The back of the apparatus is painted black and illumination is from the front; therefore, in the photographs of the experiments, the oil-bearing formation appears black, whereas the water- or gas-invaded areas are white.

Jan 1, 1958

By J. F. Myers, R. J. Tower

"There is nothing new under the sun." All over the world, mineral-dressing engineers are working at their problems, no two of which are alike. Each encounters equipment and process problems. Many devise simple ways and means of overcoming their difficulties. Many of these problems are quite common in the industry, yet, since no one human being seems capable of thinking of everything, these problems at some plants often are looked upon as necessary evils. The purpose of this symposium is to gather together, from competent engineers, devices and practices that have been useful to them. Most of the ideas contributed are not new, yet there is no plant operator, old timer or youngster, who will not find some idea herein that will give him a suggestion for improving his operation. Space does not permit a complete elaboration on all of the contributions offered. Each item is summarized, but this will be ample for those skilled in the art of mineral dressing. A list of contributors appears at the end of the paper, and the superior number at the end of each item identifies its source. General Equipment A signal light to show that a steel bin, containing relatively line, moist ore, is full, can be made by suspending a copper rod in the bin to a sufficient depth to ensure ample contact with the ore. One wire of a 32-volt circuit should be attached to the rod and one to the side of the bin. Sufficient current will flow to make the signal light burn. A 110-volt circuit could be used, but 32 volts ensures safety.10 Fig I shows a circular bin for crushed ore. It is a concrete structure footed on the ground, using no supporting columns. Tailing from the sink-float was used for aggregate. Cross conveyors for discharging ore are not required, nor is a tripper for filling. Segregation is minimized by drawing from different gates. An exhaust fan on top of the bin eliminates condensation due to temperature of the ore.21 A beam with an adjustable point of suspension near the center permits rigging rolls for removal in a very few minutes. This makes unnecessary the lacing of the cable through the hub bolts on one side, around the shaft on the other, and the trouble of balancing the load.8 The ratchet handle on a Symons crusher may be replaced by a drum with a cable wound on it. When the cable is pulled by a crane or hoist it causes the drum to revolve and thus screws or unscrews the bowl. This reduces handwork and materially shortens the time required for the job.' TO Spread ore feed from an apron feeder over a belt conveyor, place a heavy steel bar about midway between the top

Jan 1, 1949

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By R. H. Tien

This paper presents an analytical solution of the problem of freezing of a semi-infinite slab with constant surface temperature; in this analysis accoz~nt is taken of the heat evolution during the solid-state transformations in the frozen skin. The regions where transformations occur are treated as plane isothermal heat sources; i.e., the rates of transformations are assumed to be infinite. In the model considered, three plane heat sources are assumed to be present in the frozen solid. The solution yields the temperature distribution in the solid, the rates of movement of the heat sources , and the rate of movement of the solidification front. It is shown that, although the sum of the heats of transformations in the solid is about 20 or 43 pct of the heat of fusion of iron or manganese, respectively, the effect of the heat evolution in solid-state transformations on the rate of solidification is insignzficant. IN several recent mathematical studies of solidification of liquid metals'-3 no account was taken of the heat evolution accompanying the solid-state transformations. In the case of, for example, steel, there are several phase transformations 6 -y, y -a, and the magnetic transformation. Whether or not a significant error is introduced into the mathematical simulation of solidification processes by the omission of the heat effects associated with these phase transformations is not known. The purpose of the present study is to investigate the effect of these phase transformations on the temperature distribution and the rate of solidification based solely on the heat transfer point of view. That is, for the sake of simplicity, freezing of a pure metal with solid-state transformations will be considered. The mathematical model which represents the present problem includes four moving heat sources representing freezing and phase transformations, 6— y — a — ferromagnetic. The thermal properties such as conductivity and specific heat, and so forth, are different from one phase to the other. But they are considered to be uniform over any particular phase. The usual Fourier heat flow law is employed. The concept of conservation of energy is applied at every heat source in order to estimate their rate of movement. The temperature distribution in the solid and the positions where transformations occur are expressed analytically in terms of error function solutions and four coefficients which are determined from four nonlinear algebraic equations. These coefficients can be calculated either by trial and error or by any numerical method. MATHEMATICAL ANALYSIS Fig. 1 is a schematic diagram showing the zones of different phases 1, 2, 3, and 4 in the solidified portion of a semi-infinite pure liquid metal. The heat is subtracted from the system at x = 0 which is maintained

Jan 1, 1968

By M. C. Leverett

Knowledge of the theory underlying the behavior of mixtures of fluids in reservoir rocks is essential to the proper solution of certain types of problems in petroleum production, but is as yet incompletely developed. The object of this paper is to show the application of well established thermody-namic and physical principles to these problems, and thus to assist in the development of the basic theory. For convenience the problems to be considered here may be divided into two groups: 1. Static problems, involving only the static balance between capillary forces and those due to the difference in densities of the fluids; i.e., gravitational forces. 2. Dynamic problems, involving analysis of the motion oi mixtures of immiscible fluids in porous media under the influence of forces due to gravity, capillarity, and an impressed external pressure differential. Capillary Equilbrium in Sands Under this heading the static type of problem will be discussed and the results of experimental investigations on the capillary properties of unconsolidated sands will be presented. Although the discussion of this section is, in a sense, prefatory to the treatment of problems of mixture flow, the concepts developed here have considerable intrinsic importance apart from their ap-plication to flow problems. For, it is reason-able to postulate that the reservoir fluids are, owing to their long existence in undis- turbed mutual contact prior to exploitation, in substantial equilibrium. It follows that their distribution in the reservoir at the time of tapping should be entirely predictable from the theory of capillary equi librium, provided certain experimentally measurable properties of the reservoir rock are known. Knowledge of the distribution of the several fluids in the reservoir is, ol course, helpful in the estimation of reserves and in other problems. It is to be emphasized that throughout the discussion of capillary statics it is assumed that the fluids are in equilibrium from the capillary standpoint. Thus, water, where it is referred to as being in a reservoir, will be understood to be interstitial water, present at the time of drilling the reservoir, commonly termed "connate" water. The theory developed here is perfectly general for any porous solid, whether a carefully prepared unconsolidated sand or a natural sandstone from an oil reservoir. At present, however, only problems involving clean, unconsolidated sands can be made to yield numerical solutions, since only such sands have been adequately investigated experimentally. Experimental evaluation of the pertinent properties 01 natural reservoir rocks will permit the extension of the numerical treatment to problems involving these materials. We shall now consider in some detail the static equilibrium of fluid mixtures in porous solids: that is, the manner in which the reservoir fluids are distributed vertically whell the Forces due to capillarity are just balanccd by those due to gravitation.

Jan 1, 1941

By S. S. Clarke

THE sheet-ground deposits of the TriState district, because they are fairly uniform in thickness (7 to 11 ft.)-rather flat, with an easy dip to the west-and cover a large acreage, offered a problem of improved transportation. Heading advance in this kind of mine is very rapid and track haulage requires a larger crew of trackmen than do other mines, and a heavy investment in track. The use of some type of rubber-tired truck equipment for underground haulage was under consideration for some time by the Eagle-Picher Mining and Smelting Co. The nature of some ore bodies made them not adaptable to truck haulage and some mines that did offer possibilities were equipped with other types of haulage, and the expected savings by the use of trucks did not offset the loss of investment that would be incurred in discarding other equipment. The decision was made to sink a new shaft, designed for skip hoisting, on the Blue Goose ore body, and then develop truck equipment. DEVELOPING TRACTORS AND TRAILERS A study was made of internal-combustion engines for power units in the tractors, but the extreme difficulty of controlling air circulation, and the heavy cost of drilling large churn drill holes for blower installations, led to the adoption of a tractor with a storage battery. The storage-battery tractor that was on the market for mine haulage was impossible to obtain because all were needed for defense work. Several standard electric-truck chassis were purchased and rebuilt in the Eagle-Picher shops. The steering wheel was shortened and set vertical, permitting the driver's seat to be moved forward, and the frame was shortened enough to take the battery box and the fifth wheel support that carried the gooseneck of the dump trailer. The fifth wheel, or turntable, is of the ball and socket type. Fig. I shows the ball fastened to the gooseneck. The socket is split to permit introduction of the ball and is held by through-bolts, and the socket is welded to a ½ -in. plate, which in turn is attached to the tractor frame. Smaller wheels and tires were put on to reduce over-all height. If it had been necessary, the springs could have been reversed, or taken off entirely, to gain additional clearance. The tractors are equipped with 48-cell, 23-plate, 400-A.H. batteries. With the initial tonnage and mileage, the batteries were about 50 per cent down at the end of a shift. Tractors have truck tires 7.50 by 20, 8-ply, front and rear, the rear being dual. After four months of use, the tires are beginning to show signs of failure.* In

Jan 1, 1942

By Rollin Farmin

Rock pressure against the supports for underground workings in certain mines becomes sufficiently severe to crush sound timbers. The cost of maintenance of these mines increases critically as the workings are extended. "Heavy ground " and "swell-jng ground" are terms commonly applied to a condition of excessive pressure from the wall rock. Defined for the purposes of this paper, "heavy ground" delivers gravi-tative pressure on the supports of a mint opening; "swelling ground" delivers pressure arising from expansion of the wall rock. Mining problems created by heavy ground have been studied extensively by mining engineers, as in the recent Symposium on Block caving.' A parallel study of rock bursts2 attacks the field of ground that ruptures under strain. The problem of swelling ground, which has received less current attention, is the subject of this paper. An ExaMPLe of Swelling Ground Severe cases of swelling ground are found in the gougy shear zones in mines along the western Sierra Nevada, where the veins are accompanied by faults through altered serpentine, schist and slate. For example, along troublesome stretches in the ldaho Maryland mine, Grass Valley, California, swelling ground continues to crush drift timbers, with diminishing intensity, for 3 to 10 years after entry. During this period, from five to nine generations of crushed timber sets must be replaced and a large additional tonnage of scaly rock and wet gouge must be removed from the drift to make room for this succession of new timbers. After "the squeeze has been taken out of the ground" the timbers will stand for years, until they collapse from decay. Heaving of floor and footwall along drifts develops soon after the timber sets are placed and frequent grading down of the track is necessary to keep it serviceable and to maintain headroom. If sills are placed under the drift posts, the sets break more quickly and the track becomes impassable at once. When the floor is left Open? and the bottoms of posts and stulls are pencil-pointed, the scaly ground of the fault zone swells up around the timbers (Fig. I) instead of breaking them (Fig. 2). A foot or two of this encroaching ground is trimmed from the floor and lower sides of the drift several times before complete retimbering is necessary. when a set of timber fai1s under the Pressure of swelling ground, there is no immediate fall of timber and broken rock to fill the drift, as is customary in heavy, caving ground. Instead, ground swelling from sides, top and bottom gradually closes the opening, over a period of weeks or months, and no especial hazard to workmen is present while they have room to walk through the narrowing drift. Most

Jan 1, 1946

By Donald W. Scott, Adam Wesner

This paper describes the study of 23 nonmagnetic iron-formation samples from the Mesabi Range and shows the significance of their chemical, mineral, and physical properties in terms of their concentration. Data presented here resulted from a research project carried out from 1942 to 1952 by 10 major producers of iron ore, working in conjunction with Battelle Memorial Institute. THE inevitable depletion of Mesabi direct-shipping iron ores, hastened by recent wars, has increased the importance of developing methods to concentrate iron-formation materials. Many mining companies, independent research organizations, chemical companies, and equipment manufacturers are devoting attention to this important work. It is only natural that magnetic iron-formation materials have received major emphasis, since magnetic recovery methods apply and reserves of Mesabi magnetic taconites are large. However, the nonmagnetic* iron-formation materials are likewise believed to represent a large reserve and their study has not been neglected. tions over the years have shown that in addition to the unenriched taconite, which is dense and hard, and the direct-shipping ore, there are transition taconites grading into the friable wash, or intermediate ores. The transition taconites are less massive than the unaltered taconites and usually coarser-grained. This variation, coupled with the fact that there were no extensive drillings in the unaltered taconite, posed a most difficult problem of obtaining samples that would be representative of large tonnages of the fresh rock. The problem was increased by the tremendous extension of the nonmagnetic formation materials on the Mesabi and by the question of their accessibility to mining. A drilling program was evolved that would surmount these difficulties. Selection of samples was made by a committee representing producers in the area. The samples were procured from 1—taconite walls near bodies of stripping burden or wash ore and 2—from shafts in the process of being sunk through taconite for drainage or mining operations. Most of the samples were obtained from the cherty horizons because it became obvious early in the program that the slaty horizons represented an exceedingly difficult concentration problem, owing to the character of the gangue minerals and the fine grind required for liberation of the valuable minerals. More samples were procured from the lower cherty horizon than from the upper cherty because it was more accessible to mining. It is not known how well the samples selected represent the nonmagnetic iron-formation material. However, they were chosen by people Well acquainted with the geology of the Mesabi range and the mining problems involved. It is believed that they represent a fair cross-section of the types of materials that will be encountered. Table I gives data on the origin of the 23 samples and the horizon footages from which they were obtained. Samples 1 through 10, and 15 and 16

Jan 1, 1955

By E. W. McAllister

The decision of the California Oil Umpire's' office to accept well potentials established from subsurface-pressure data has brought to the attention of many operators for the first time the application of such data to production problems. This paper reviews the development and application of subsurface-pressure data in kettleman Hills, where these data have been used in production work since 1932. The Kettleman Hills field was discovered in October 1928. The first subsurface-pressure surveys were made early in 1932 and by the middle of 1933 the two major operators in the field were making routine pressure runs in thcir respective wells. Shortly therefter, these companies agreed to exchange pressure data, and later a third company entered into the agreement. This made it possible to analyze the effects upon the reservoir pressure of past production practices, which are discussed in the latter part of the report. It is interesting that many of the applications of subsurface-pressure data discussed herein were anticipated by C. L. Clark and C. B. Kimberlint in a report2 dated March 1933. PRODUCTIVITY Index In the majority of individual well problems involving the use of subsurface- pressure data, it is necessary to use a factor known as the "productivity index," which indicates the ability of a well to produce and represents the number of barrels of oil or oil and water per day that will enter the well bore for each pound per square inch pressure drop made opposite the producing interval of the well. The productivity index may be determined from pressure and production data for one or more rates of flow and a static or shut-in pressure survey or from production and pressure data for two or more rates of flow. Productivity indices may be based upon either net oil or total fluid production. All indices referred to in this report are based upon net oil. The value of the productivity index for Kettlcman Hills wells decreases generally with time and it is not uncommon for the index to vary in value at any specific time fur various rates of flow. The decline of the productivity index may be attributed partly to the loss of reservoir pressure. As the reservoir pressure decreases, gas originally in solution is released from the oil, congesting the flow of fluids through the formation and increasing the viscosity and surface tension of the oil; thus the flow resistance of the fluids through the formation is increased, resulting in a decrease of the productivity index. For convenient reference, the productivity indices for each well are plotted against time and a curve is drawn through the points showing the trend of the average index value. Plotted on Fig. I are index values for five

Jan 1, 1941

By E. W. McAllister

The decision of the California Oil Umpire's' office to accept well potentials established from subsurface-pressure data has brought to the attention of many operators for the first time the application of such data to production problems. This paper reviews the development and application of subsurface-pressure data in kettleman Hills, where these data have been used in production work since 1932. The Kettleman Hills field was discovered in October 1928. The first subsurface-pressure surveys were made early in 1932 and by the middle of 1933 the two major operators in the field were making routine pressure runs in thcir respective wells. Shortly therefter, these companies agreed to exchange pressure data, and later a third company entered into the agreement. This made it possible to analyze the effects upon the reservoir pressure of past production practices, which are discussed in the latter part of the report. It is interesting that many of the applications of subsurface-pressure data discussed herein were anticipated by C. L. Clark and C. B. Kimberlint in a report2 dated March 1933. PRODUCTIVITY Index In the majority of individual well problems involving the use of subsurface- pressure data, it is necessary to use a factor known as the "productivity index," which indicates the ability of a well to produce and represents the number of barrels of oil or oil and water per day that will enter the well bore for each pound per square inch pressure drop made opposite the producing interval of the well. The productivity index may be determined from pressure and production data for one or more rates of flow and a static or shut-in pressure survey or from production and pressure data for two or more rates of flow. Productivity indices may be based upon either net oil or total fluid production. All indices referred to in this report are based upon net oil. The value of the productivity index for Kettlcman Hills wells decreases generally with time and it is not uncommon for the index to vary in value at any specific time fur various rates of flow. The decline of the productivity index may be attributed partly to the loss of reservoir pressure. As the reservoir pressure decreases, gas originally in solution is released from the oil, congesting the flow of fluids through the formation and increasing the viscosity and surface tension of the oil; thus the flow resistance of the fluids through the formation is increased, resulting in a decrease of the productivity index. For convenient reference, the productivity indices for each well are plotted against time and a curve is drawn through the points showing the trend of the average index value. Plotted on Fig. I are index values for five

Jan 1, 1941

By E. W. McAllister

THE decision of the California Oil Umpire's1 office to accept well potentials established from subsurface-pressure data has brought to the attention of many operators for the first time the application of such data to production problems. This paper reviews the development and application of subsurface-pressure data in Kettleman Hills, where these data have been used in production work since 1932. The Kettleman Hills field was discovered in October 1928. The first subsurface-pressure surveys were made early in 1932 and by the middle of 1933 the two major operators in the field were making routine pressure runs in their respective wells. Shortly thereafter, these companies agreed to exchange pressure data, and later a third company entered into the agreement. This made it possible to analyze the effects upon the reservoir pressure of past production practices, which are discussed in the latter part of the report. It is interesting that many of the applications of subsurface-pressure data discussed herein were anticipated by C. L. Clarks and C. B. Kimberlin‡ in a reports dated March 1933. PRODUCTIVITY INDEX In the majority of individual well problems involving the use of subsurface pressure data, it is necessary to use a factor known as the "productivity index," which indicates the ability of a well to produce and represents the number of barrels of oil or oil and water per day that will enter the well bore for each pound per square inch pressure drop made opposite the producing interval of the well. The productivity index may be determined from pressure and production data for one or more rates of flow and a static or shut-in pressure survey or from production and pressure data for two or more rates of flow. Productivity indices may be based upon either net oil or total fluid production. All indices referred to in this report are based upon net oil. The value of the productivity index for Kettleman Hills wells decreases generally with time and it is not uncommon for the index to vary in value at any specific time for various rates of flow. The decline of the productivity index may be attributed partly to the loss of reservoir pressure. As. the reservoir pressure decreases, gas originally in solution is released from the oil, congesting the flow of fluids through the formation and increasing the viscosity and surface tension of the oil; thus the flow resistance of the fluids through the formation is increased, resulting in a decrease of the productivity index. For convenient reference, the productivity indices for each well are plotted against time and a curve is drawn through the points showing the trend of the average index value. Plotted on Fig. I are index values for five

Jan 1, 1941

By John Lamont, Walter Crafts

The principle formulated by Grossmannl for calculating hardenability of steel by multiplying the ideal diameter of "pure" iron-carbon alloys by factors for grain size and alloying elements has been confirmed on many steels and has proved useful in designing substitute alloy steels. Grossmann found that the typical behavior of the multiplying factors was to increase directly in proportion to the amount of the alloy present in a steel. However, the multiplying factor for the effect of silicon on hardenability was found by Grossmann to increase to a lesser degree as the amount of silicon was increased. In view of the increasing use of silicon in heat-treating steels, the effect of silicon on hardenability is becoming more important. Calculation of the hardenability of high-silicon steels made at the Union Carbide and Carbon Research Laboratories, Inc., indicated that the multiplying factor for silicon increased directly in proportion to the amount of silicon present. A more extended study of high-silicon steels covering fairly wide ranges of grain size, carbon, manganese, and aluminum has confirmed that up to 2 per cent silicon the multiplying factor is directly proportional to the silicon content. Manganese and aluminum factors have also been! determined. The results of the study offer strong confirmation of the general validity of Grossmann's multiplying principle. Testing Procedure Steels on which the study of the effect of silicon on hardenability was based were made in high-frequency induction furnaces using Armco iron and standard alloying materials. The ingots were forged to bars, and sections were normalized prior to machining Jominy hardenability test specimens. The Jominy test was carried out under standard conditions.2 The depth of hardness penetration for determination of ideal diameter at "half hardness" was taken at the hardness level indicated in Fig. 29 in Grossmann's paper by the solid line for 50 per cent martensite in plain carbon steel. The depth of penetration of hardness on the Jominy specimen was converted to ideal diameter by the relation given in Fig. 28 of Grossmann's paper. Chemical analysis was determined on a sample taken adjacent to the Jominy specimen. Aluminum was determined as "acid-soluble aluminum" rather than as total aluminum, as it is probably more representative of the aluminum that is effective as an alloying agent. In addition to the elements nominally present in the steels, analyses were made for residual phosphorus, sulphur, nickel, copper, molybdenum and chromium on one heat of those made with the same materials during the same period. Actual grain size was determined by microscopic examination of small samples quenched in water after receiving the same thermal cycle as the Jominy hardenability specimens. Chemical analyses, heat-treatment, grain size, and hardenability are shown in Table I representing three ranges of composition.

Jan 1, 1943

By John Lamont, Walter Crafts

The principle formulated by Grossmannl for calculating hardenability of steel by multiplying the ideal diameter of "pure" iron-carbon alloys by factors for grain size and alloying elements has been confirmed on many steels and has proved useful in designing substitute alloy steels. Grossmann found that the typical behavior of the multiplying factors was to increase directly in proportion to the amount of the alloy present in a steel. However, the multiplying factor for the effect of silicon on hardenability was found by Grossmann to increase to a lesser degree as the amount of silicon was increased. In view of the increasing use of silicon in heat-treating steels, the effect of silicon on hardenability is becoming more important. Calculation of the hardenability of high-silicon steels made at the Union Carbide and Carbon Research Laboratories, Inc., indicated that the multiplying factor for silicon increased directly in proportion to the amount of silicon present. A more extended study of high-silicon steels covering fairly wide ranges of grain size, carbon, manganese, and aluminum has confirmed that up to 2 per cent silicon the multiplying factor is directly proportional to the silicon content. Manganese and aluminum factors have also been! determined. The results of the study offer strong confirmation of the general validity of Grossmann's multiplying principle. Testing Procedure Steels on which the study of the effect of silicon on hardenability was based were made in high-frequency induction furnaces using Armco iron and standard alloying materials. The ingots were forged to bars, and sections were normalized prior to machining Jominy hardenability test specimens. The Jominy test was carried out under standard conditions.2 The depth of hardness penetration for determination of ideal diameter at "half hardness" was taken at the hardness level indicated in Fig. 29 in Grossmann's paper by the solid line for 50 per cent martensite in plain carbon steel. The depth of penetration of hardness on the Jominy specimen was converted to ideal diameter by the relation given in Fig. 28 of Grossmann's paper. Chemical analysis was determined on a sample taken adjacent to the Jominy specimen. Aluminum was determined as "acid-soluble aluminum" rather than as total aluminum, as it is probably more representative of the aluminum that is effective as an alloying agent. In addition to the elements nominally present in the steels, analyses were made for residual phosphorus, sulphur, nickel, copper, molybdenum and chromium on one heat of those made with the same materials during the same period. Actual grain size was determined by microscopic examination of small samples quenched in water after receiving the same thermal cycle as the Jominy hardenability specimens. Chemical analyses, heat-treatment, grain size, and hardenability are shown in Table I representing three ranges of composition.

Jan 1, 1943

By V. S. Tuman

In the first part of this paper, an estimate is made of the magnitude and extent of the thermal stresses which result from mud circulation. Our study is made for the period of relaxation, i.e., when the drilling operations are terminated and mud circulation is discontinued. In the second part, we have shown how the thermal stress can affect the wave propagation. An example is worked out for a Carbondale sandstone (Illinois basin). It is concluded that, in extreme cases when differential temperature is about 100°F, the travel time will be affected by about 2 microsec/ft. For more refined permeability studies, such corrections would be desirable. MAGNITUDE AND EXTENT OF THERMAL STRESSES RESULTING FROM MUD CIRCULATION When geological beds are penetrated by boreholes, it is observed that the formation temperatures increase with depth; however, the temperature profile varies considerably from place to place. During drilling operations, mud pumped from a pit at atmospheric temperature absorbs heat from the lower beds. As a result, the drilling fluid returning to the surface is at a higher temperature than the surrounding beds. The temperature gradient in a well depends on the rate of mud circulation and other factors; normally, this temperature gradient is smaller than the natural gradient in the formations. (See Fig. 1.) The temperature difference between the mud column and the surrounding beds gives rise to therma1 stresses (which are also important in the phenomenon of fracturing), and it is expected that they will affect the transit time of the sonic front in velocity logging.1 It is evident chat beds near the surface will undergo various cycles and will have a complicated dynamical and thermal-stress history. A limestone bed which is just penetrated will act as a source of heat, warming up the cold mud pumped down a few minutes earlier from the surface pit. The same limestone bed a week later will act as a sink, absorbing heat from the drilling mud which has already warmed up sufficiently to be at a higher temperature than the bed in question. No doubt a large section of the hole will undergo a heat treatment, which will make the calculation of the exact magnitude of the thermal stresses very difficult. In the solution of wellbore thermal equation, it is assumed that the rock around the wellbore is elastic and isotropic, and that the system is radially symmetrical. A complete dynamical solution of the thermal stresses set up at different horizons during the drilling operations would require a comprehensive history of the mud circulation, the surface temperature of the pit and the number of hours in which mud was not circulated. CONDUCTION OF HEAT AND THERMAL EQUATION OF STATE

By J. Szekely

A rrlethod is presented for the estitnation of oxygen pickup by teettzed molten steel streams. Of the mechanisrt~s considered for oxygen absorption, physical entrainment appeared to be the most significant. The estent of this physical entrainment may be calculated by the application of boundary layer theory. It was found that the values of oxygen pickup thus predicted were in wry good agreement with data reported in the literature, in the case of short, well-defined metal streams. This entrainment model does not provide an adequate description of oxygen pickup by long streams, exoosed to external winds and where breakup of the streatn is likely. WheN molten steel is teemed into a mold or tundish it will absorb oxygen contained in its environment. Recently interest has been expressed in the measurement and possible prediction of the extent of this oxygen absorption: this interest owes its existence to two principal factors: a) the desirability of providing a quantitative assessment of the role played by the absorbed oxygen in impairing the quality of (vacuum degassed. stainless, or continuously cast) steel; b) the need for providing guidelines for stream protection methods. The purpose of this communication is to suggest a simple method for the prediction of oxygen absorption by continuous metal streams and to compare the predicted values with the data available in the literature. It is hoped that this method may provide at least an initial framework for the interpretation of additional data that might become available. FORMULATION Consider a continuous metal stream falling into a molten metal pool as depicted in Fig. 1. This system may absorb oxygen due to the following two mechanisms: 1) physical entrainment of gases (including oxygen) into the molten pool where reactions. thus absorption, will occur; 2) mass transfer (convec:tive diffusion) of oxygen to the metal stream. 1) Physical Entrainment. The physical entrainment may be calculated by using the concept of the diaplace-ttzent tlzickness of the laminar boundary layer, which will be stated briefly in the following.&apos; When a fluid flows past a solid surface, a portion of the fluid close to the surface is retarded due to fric-tional forces. This region in which the velocity of the fluid differs from that in the main stream is called the boundary layer. An illustration of this is given in Fig. 2 where it is seen that the thickness of the boundary layer increases as we move along in the x direction. In the laminar region, when Re, < 10&apos; the thickness of the boundary layer is given by the following relationship: f =4.64 Re;1" [1] where 61 is the boundary layer thickness, x is the length along the leading edge, Us is the velocity of the free stream, (i is the viscosity of the fluid (gas in this instance).

Jan 1, 1970

By Thomas Fraser, H. F. Yancey

Prior to the war just ended, Germany was the greatest coal producer in continental Europe. In 1943 the production of coal, bituminous and higher in rank, together with brown coal calculated to the equivalent amount of bituminous coal, is estimated to have been about 240 million metric tons, according to the War Department. Before the war production in Germany exceeded consumption. No other country in continental Europe except Poland had a large surplus. However, England&apos;s surplus was the largest in Europe as a whole. Before World War II the Ruhr Basin normally supplied about 70 pet of the total production of high-rank coal, the Saar and Aachen about 6 pet each, Upper Silesia about 14 pet, and Silesia and Saxony the remainder. Nearly one third of the brown coal was produced in the Rhineland, a little less than one half in central Germany nest of the Elbe River, and about one fourth east of the Elbe. Bituminous coal and brown coal together constituted by far the most important energy resources of the old German Reich. Bituminous coal furnished nearly 70 pet of the total energy requirement, brown coal supplied about 25 pet, and water power, wood, petroleum and alcohol together aggregated only 7 pet. Because it was the most important single mineral resource of Germany, an excess of coal enabled the Reich to import nearly all the other mineral products that she lacked, such as iron ore from Lorraine. The area adjacent to the coal fields was supplied with gas from an interconnected grid. Similar electric grids are based on brown coal with the power stations at the mines. Coal tar provided the foundation for the development of the extensive German chemical industries as exemplified by the I. G. Farbenindustrie. For almost a century, German scientists have been adequately supported both by the State and by industry in studying improved methods of utilizing coal. In Germany the mineral rights were reserved by the State and ordered eatraction of coal was enforced. Each lease comprised a relatively extensive area. which accounts for the generally large size of the mines and mining companies In 1938 there were 160 mines in the Ruhr, with a total output of 125 million tons but 90 pet of the production was controlled by 20 companies. By far the largest single coal-mining company in Germany was the Gelsen-kirchener Bergwerke A. G., which produced nearly 27 million tons in the Ruhr in 1937. Second was Saargruben A. G. a State-owned company operating in the Saar, which produced &apos;lore than &apos;3 million tons. Third was Bergwerksgesellschaft Hibernia A. G., with 10 million tons, also in the Ruhr. Briquettes are made from both bitumillous coal and brown coal, but in 1938 some 44 million toils of brown-coal bri-

Jan 1, 1947

By Thomas Fraser, H. F. Yancey

Prior to the war just ended, Germany was the greatest coal producer in continental Europe. In 1943 the production of coal, bituminous and higher in rank, together with brown coal calculated to the equivalent amount of bituminous coal, is estimated to have been about 240 million metric tons, according to the War Department. Before the war production in Germany exceeded consumption. No other country in continental Europe except Poland had a large surplus. However, England&apos;s surplus was the largest in Europe as a whole. Before World War II the Ruhr Basin normally supplied about 70 pet of the total production of high-rank coal, the Saar and Aachen about 6 pet each, Upper Silesia about 14 pet, and Silesia and Saxony the remainder. Nearly one third of the brown coal was produced in the Rhineland, a little less than one half in central Germany nest of the Elbe River, and about one fourth east of the Elbe. Bituminous coal and brown coal together constituted by far the most important energy resources of the old German Reich. Bituminous coal furnished nearly 70 pet of the total energy requirement, brown coal supplied about 25 pet, and water power, wood, petroleum and alcohol together aggregated only 7 pet. Because it was the most important single mineral resource of Germany, an excess of coal enabled the Reich to import nearly all the other mineral products that she lacked, such as iron ore from Lorraine. The area adjacent to the coal fields was supplied with gas from an interconnected grid. Similar electric grids are based on brown coal with the power stations at the mines. Coal tar provided the foundation for the development of the extensive German chemical industries as exemplified by the I. G. Farbenindustrie. For almost a century, German scientists have been adequately supported both by the State and by industry in studying improved methods of utilizing coal. In Germany the mineral rights were reserved by the State and ordered eatraction of coal was enforced. Each lease comprised a relatively extensive area. which accounts for the generally large size of the mines and mining companies In 1938 there were 160 mines in the Ruhr, with a total output of 125 million tons but 90 pet of the production was controlled by 20 companies. By far the largest single coal-mining company in Germany was the Gelsen-kirchener Bergwerke A. G., which produced nearly 27 million tons in the Ruhr in 1937. Second was Saargruben A. G. a State-owned company operating in the Saar, which produced &apos;lore than &apos;3 million tons. Third was Bergwerksgesellschaft Hibernia A. G., with 10 million tons, also in the Ruhr. Briquettes are made from both bitumillous coal and brown coal, but in 1938 some 44 million toils of brown-coal bri-

Jan 1, 1947

By T. E. Leontis, D. H. Feisel

MAGNESIUM alloys containing rare earth metals have received considerable attention during the past several years because of the need for light alloys having high strength and creep resistance at elevated temperatures. Although much of the work reported earlier has dealt with alloys containing Mischmetal, it has been shown in two previous papersl, V hat distinctly different effects are produced by various rare earth metals and rare earth metal mixtures on the properties of magnesium. For example, much higher strengths are obtained in magnesium alloys containing didym-ium (essentially neodymium plus praseodymium) than in alloys made with Mischmetal, which contains all the rare earth metals in the proportions in which they occur naturally in the monazite ore. Mg-rare earth metal alloys are characterized by a relatively coarse grain size, which greatly impairs castability. The addition of zirconium as a second alloying ingredient has been shown8,7 to refine the grain size, which also produces a distinct improvement in the strength properties. Certain Mg-Mischmetal-Zr and Mg-Mischmetal-Zn-Zr alloy compositions which are currently being produced commercially have been discussed in dytail by Nelson and Strieter,8,4 who also present some in- formation on a Mg-low Ce-Mischmetal-Zr alloy, and by Nelson.8 A patent issued to Jessup, Emley, and Fisher9 emphasizes the superiority of Mg-didymium-Zn-Zr alloys over the corresponding alloys made with Mischmetal. The purpose of this paper is to present the results of an extensive investigation concerned with the effect of increasing amounts of zirconium on magnesium sand casting alloys containing several different rare earth metal mixtures in varying amounts. The effect of the addition of zinc to some of these alloys is also being reported. Preparation and Testing of Alloys The alloys studied in this investigation were prepared in small laboratory melts according to the melting procedures described by Nelson1" as the Crucible Method. Electrolytic magnesium having the composition shown in Table I was used as the starting material. The rare earth metal alloying ingredients used in preparing these alloys were essentially of the compositions listed in Table 11. Some of the didymium-containing alloys were prepared using a Mg-didymium hardener. The rare earth metal content of this hardener analyzed 1.2 pct Ce, 10.4 pct Pr, 80.8 pct Nd, and 7.6 pct La. The zirconium was added in one of three forms: 1) as sponge zirconium obtained from the Bureau of Mines; 2) as a fused salt consisting of 50 pct ZrCl, and 50 pct alkali chlorides from which the zirconium is reduced by the magnesium; or 3) as a Mg-Zr hardener. The alloying procedures and melt hand-

Jan 1, 1958