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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 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. J. Burgess, A. R. Ramey, A. R. Adams

During interpretation of pressure buildup tests on gas wells in a tight dolomite gas reservoir, peculiar behavior was noticed. Two straight lines were apparent. Effective permeability to gas taken from either straight line was about the same, and the Miller-Dyes-Hutchinson dimensionless time check for the straight line was proper for both straight lines. Geological data indicated the likelihood of scattered trending fractures in the reservoirs. Since the first straight Iine yielded permeability values close to the geometric mean permeability from core analyses, it was postulated that the reservoir model was that of an acidized well completed in the tight dolomite, but that widely scattered hairline fractures caused the mean permeability of the reservoir distant from the well to be higher than the matrix permeability. Because all other studies of fractured reservoirs to the authors' knowledge assumed that the fracture matrix was dense enough to communicate directly with the well, no interpretative methods were available. The Hurst line-source solution for a radial change in permeability for interference between oil reservoirs was adapted to pressure buildup testing. The result indicated that the first straight line should yield the proper matrix permeability and wellbore skin effect. The second straight line may be extrapolated to obtain static pressure. The time of bend between the straight lines was used to estimate distance to a fracture. Application to field test data is shown. It is believed that the methods developed and the case history presented will add to present tools available for pressure buildup interpretation. Introduction Since the pioneer studies by Miller, Dyes, and Hutchin-son1 and Horner' in 1950 and 1951, well test analysis has become recognized as one of the most powerful tools available to both production and reservoir engineers. Well test analysis serves as a logical basis for well stimulation and completion analysis, and for long-term reservoir engineering. Since the early 19501s, much effort has been placed on the development of well-test analytical methods. Reservoir and well conditions of increasing complexity have been considered systematically to provide the analyst with a catalog of causes and effects. Matthews and Russella state that some 200 papers dealing with this subject have been published in the last 35 years. Developments in well test analysis appear to have originated in one of two ways. Either a physically realistic field condition was anticipated and analytical solutions for the condition achieved, or anomalous field test behavior was recognized and interpretative methods sought for the anomaly. In recent years, it has appeared that the latter has inspired an increasing number of studies. The analyst today finds an increasing number of known cause and effect studies available for well test analysis, the classic of which is that of finding the specific flow problem that generated the answer — the well behavior. Although it may be impossible to achieve this goal uniquely, the analyst often is able to select a useful interpretation that combines all known performance and geologic data — or to show that various logical alternatives would not significantly affect the interpretation. During a recent reservoir study, we observed gas well test behavior that did not appear to fit behavior described previously. Although it cannot be said that we have found a unique interpretation, we shall present in this paper the peculiar behavior observed, and describe the reservoir and interpretative methods developed. Reservoir Description The subject gas reservoir is a 9-mile-long, narrow dolomite reservoir lying within a limestone of Ordovician age. (See Fig. 1.) The dolomitized rock in the field consists of dark brown to buff, dense to coarsely crystalline, vugular dolomite containing numerous hairline fractures, many of which may have been closed in the reservoir and parted when cores were brought to the surface. Larger fractures are also apparent in core, but usually are filled and sealed with euhedral dolomite crystals. Portions of the north flank of the reservoir are known to be cut by a sealing fault downthrown to the north. Gas wells located near the fault have higher open flow potentials than those more distant from the fault. This is believed to be a result of higher permeability near the fault due to more extensive and open fractures. Detailed coring and core analysis have been performed on several of the wells in this reservoir. Fig. 2 presents permeability variation' plots for both horizontal and vertical

Jan 1, 1969

By H. E. Stauss

THE time-to-fracture test has been applied to pure platinum and to two alloys of platinum under the special conditions of small cross-sectional area of the specimens and of a test temperature above the annealing temperature. While the results are similar in character to those secured with large specimens of steel at temperatures below the annealing temperatures, two differences are noted: (I) an upward inflection in the curves for log stress vs. log time for the alloys, and (2) a sharp break in the curve for log stress vs. log time for pure platinum when single crystals filled the wire. The experiments showed that: (I) platinum and 10 per cent rhodium-platinum maintained their strengths at 1100°C. better than did 10 per cent iridium- platinum, and (2) the rhodium-platinum after a time exceeded the iridium-platinum in strength at 1100°C. Platinum alloys in their service at high temperatures encounter conditions some- what similar to those that exist in the usual form of the time-to-fracture "l test with steel. This paper is intended primarily to present results obtained by a "time-to- fracture" test under conditions approximating actual service for platinum (at the temperature 1100°C. under oxidizing conditions) with three materials, pure platinum (99.99 per cent), a platinum alloy with lo per cent iridium, and a platinum alloy with 10 per cent rhodium. The experimental procedure differed from that previously used in this type of measurement in that the samples were of small diameter (0.010 in.), were fully annealed, and were tested at a temperature definitely above their annealing points (600°C., 1000°C. and 1050°C., respectively, for 60 per cent cold reduction and 15 min. heating time2,3). The experimental arrangement was similar to that previously described,4 using as heating unit a small, horizontal, platinum- wound furnace, ½ by 12 in., maintained at constant temperature by an automatic controller. The samples were 0.010-in. wires, which had been annealed at 1200°C. by drawing them slowly through the furnace. The time-to-fracture was measured electrically. Elongation was not determined because of the difficulties inherent in the experimental arrangement. Life-that is, the time-to-fracture-was considered the important property in these first tests. No attempt was made to measure the reduction in area, but the types of fracture were noted qualitatively; in the text they are referred to as (I) the normal, plastic, or necked fracture, (2) the knife-edge fracture, and (3) the brittle or intercrystalline fracture with small reduction of area. Results for different constant applied stresses are plotted in Fig. I. In all cases at least two trials were made for each stress, although they cannot always be indicated separately on the curves. The breaking stresses drop very rapidly to a small frac-

Jan 1, 1943

By J. H. Hollomon, L. D. Jaffe, M. R. Norton

In the practical heat-treatment of steel the decomposition of austenite usually occurs during cooling rather than at constant temperature. Nevertheless, the course of this decomposition has generally been studied only isothermally. Isothermal studies are not only simpler experimentally, but have the great theoretical advantage that one of the variables, temperature, is constant. It is the purpose of this paper to outline the principles that govern the relations between isothermal and anisothermalt‡ decomposition of austenite, to present and systematize the available experimental information, and to indicate the gaps in the existing knowledge. Some of the experimental information is the result of new work.§ Most of it is derived from scattered data in the literature. Many of these data were obtained incidentally in the course of research on other subjects and their significance has not been pointed out and perhaps not understood. It is hoped that this paper will aid future planning of more extensive research on anisothermal decomposition. Method In order to study the relations between isothermal and anisothermal decomposition, it appears fruitful to view anisothermal decomposition as taking place at a series of constant temperatures1 (except for the martensite reaction, which does not occur isothermally to an appreciable extent). When the time the steel is at each temperature is finite, the over-all amount of the reaction is considered to be the sum of the amounts occurring at each of the successive temperatures. During continuous cooling or heating, the time the steel is at each temperature and the difference between successive temperatures can be considered to approach zero. The over-all amount of transformation will then be given by integration over the range of temperatures involved. This point of view is advantageous in that it considers anisothermal transformation to be a series of isothermal transformations. The problem thus becomes one of determining the effect of partial decomposition at any given temperature upon subsequent decomposition at another temperature. Single Anisothermal Reaction Consider a phase brought to a temperature at which it is unstable, held there until it has partially transformed, and then brought to another temperature at

Jan 1, 1947

By L. D. Jaffe, M. R. Norton, J. H. Hollomon

In the practical heat-treatment of steel the decomposition of austenite usually occurs during cooling rather than at constant temperature. Nevertheless, the course of this decomposition has generally been studied only isothermally. Isothermal studies are not only simpler experimentally, but have the great theoretical advantage that one of the variables, temperature, is constant. It is the purpose of this paper to outline the principles that govern the relations between isothermal and anisothermalt‡ decomposition of austenite, to present and systematize the available experimental information, and to indicate the gaps in the existing knowledge. Some of the experimental information is the result of new work.§ Most of it is derived from scattered data in the literature. Many of these data were obtained incidentally in the course of research on other subjects and their significance has not been pointed out and perhaps not understood. It is hoped that this paper will aid future planning of more extensive research on anisothermal decomposition. Method In order to study the relations between isothermal and anisothermal decomposition, it appears fruitful to view anisothermal decomposition as taking place at a series of constant temperatures1 (except for the martensite reaction, which does not occur isothermally to an appreciable extent). When the time the steel is at each temperature is finite, the over-all amount of the reaction is considered to be the sum of the amounts occurring at each of the successive temperatures. During continuous cooling or heating, the time the steel is at each temperature and the difference between successive temperatures can be considered to approach zero. The over-all amount of transformation will then be given by integration over the range of temperatures involved. This point of view is advantageous in that it considers anisothermal transformation to be a series of isothermal transformations. The problem thus becomes one of determining the effect of partial decomposition at any given temperature upon subsequent decomposition at another temperature. Single Anisothermal Reaction Consider a phase brought to a temperature at which it is unstable, held there until it has partially transformed, and then brought to another temperature at

Jan 1, 1947

Flexibility is the keynote in designing modern exploration drills that and mobility. Add to the flexibility of individual drills the wide range of models, and the man looking for a drill has ample choice today. Weight? Choose from models as light as 50 lb or as heavy as 10,000 lb. Hole capacity? From less than 1 in. for smallest core drills to 20 in. or more for auger types. Transportation? The lightest go by packsack (in fact, that is one trade name) ; others are designed to go by Jeep, truck, on skids or are built on light trailers. Power? Select air power, gasoline or diesel engine, electric motor, or use a power take-off from the vehicle on which the drill is mounted. Drill bits offer almost as much variety as the drilling machines themselves. Many drills are suitable for a variety of uses, and often adapt to several types of bits with ease. Some of the types available are: diamond core, diamond reaming, rotary, auger, shot, and special soil sampling tools.

Oct 1, 1955

By C. A. Heiland

MEASUREMENTS of gravity with gravimeters have come into increased use in this country and abroad in the past five years. Probably 100 to 125 gravimeter parties are working in the United States alone. In oil exploration, gravimeter methods have relegated the gravity pendulum definitely to second place, if not third, and now closely rival and possibly surpass the torsion balance in many applications. Gravimeters have lately been applied in mining, although it is doubtful whether they will ever replace electrical or magnetic methods in this work. Notwithstanding the widespread application of gravimeters, there has been no article covering the entire field in the domestic or foreign literature. The purpose of this paper is to meet the demand for com-prehensive engineering information on the subject. The working principles of a number of gravimeters will be, illustrated and treated in relation to the action of corresponding seismometers and astatization methods. The mathematical discussion of theory has been confined to the most necessary fundamentals and been given in as ele-mentary form as possible. A description of calibration methods con-stitutes the last part of the paper. The symbols shown at the top of page 2 will be used in equations throughout the paper.

Jan 1, 1939

THE purpose of this chapter is to present a general outline of the basic open-hearth process for the benefit of students, practicing open-hearth operators, and metallurgists who wish to review the subject. The discussion is limited to a description of the sequence and purpose of the operations, illustrated by data and examples. Subsequent chapters deal with more detailed and fundamental studies of the subject. The function of the basic open-hearth furnace is to convert various types of ferrous material into finished steel of given composition and quality. In comparison with other steel-making methods, the basic open-hearth process is one of the most versatile, both from the stand- point of the raw materials that can be used and the types of steel that can be produced. The process can be considered as a sequence involving melting, refining, and deoxidation. In the case of some types of liquid-metal charges the melting stage is not present, but refining and deoxidation in varying degrees are fundamental features of the process. GENERAL DISCUSSION OF THE BASIC OPEN-HEARTH PROCESS The first consideration in open-hearth practice is the type of charge on which the operation is based. This consists of three components-fluxing, oxidizing, and metallic materials. Fluxes. In the basic process the fluxing material is primarily lime, added in the form of either limestone (CaC03) or burnt lime (CaO). This is supplemented by magnesia (MgO) and lime from the furnace bottom and banks. The function of these fluxes is to form a slag with the silica (SO2), manganese oxide (MnO), iron oxides (FeO and Fe203), and phosphorus oxide (P205) that are produced by the oxidation of varying amounts of the silicon, manganese, iron, and phosphorus in the charge during melting and refining. The slag, composed of the basic fluxes and the neutral and acid oxides, floats on top of the steel bath when the charge is melted. The composition of this slag depends on the amount of each slag-forming element present in the charge and on the extent of oxidation of these elements during the course of the

Jan 1, 1944

By C. E. Lesher

THIS paper reports a study of the reactivity of 950°F and 1650°F cokes as measured by relative rates of reduction of iron oxides at temperatures up to 2200°F. Previous work cited shows general acceptance of the theory that reduction by carbon is a gaseous reaction, and that kind and character of carbon as well as particle size have measurable effect on the velocity of reaction. As will be shown, the data obtained in this study con firm those conclusions. The work was not designed to examine iron oxide reduction equilibrium, but if reaction velocity be defined as the speed with which "a reaction tends to approach conditions of equilibrium," the data here presented may be considered as a study of reaction rates, and the relative degree of reduction to metallic iron as the measure of reactivity.

Jan 7, 1950

By Alfred L. Beebe

to. A strip of thin platinum foil, about one inch square, is perforated with pin-holes over its entire surface. It is then bent into the shape of a letter U, and its opposite corners are connected by short pieces of platinum wire, so as to form a sort of basket. In this is placed a piece of amalgamated zinc of convenient size, and the whole is suspended by a stout platinum or silver wire in the bottle containing the solution to be reduced. Another strip of platinum foil,

Jan 1, 1886

By N. H. MacMillan, W. M. Mularie, R. E. Jackson, A. R. C. Westwood

The initial results of a study of the environment-sensitive microhardness and diamond rotary drilling behavior of granite and its constituent minerals quartz and feldspar (microcline)1 have established that many similarities exist between the environment-sensitive mechanical (chemomechanical) behavior of these materials and that of the simpler solids such as periclase, soda-lime glass, and alumina4 studied previously, at least as far as n-alcohol (straight-chain alcohol) environments are concerned. The results of this study (hereafter designated study I) also suggested that the rate of drilling of granite in these environments is controlled by the chemomechanical behavior of its quartz constituent, and is greatest in those environments which impart a zero l-potential to this phase, thereby maximizing its hardness. Now, cationic surface-active species strongly influence the l-potentials of silicate minerals. For this reason they are widely used in mineral separation operations. In particular, dodecyl trimethyl ammonium bromide (DTAB) was found in study I to produce f 0 for quartz at a concentration in water of 107 to 10-4 moles per 1. Accordingly, the influence of dilute aqueous solutions of this surfactant on the drilling behavior of granite also was examined in study I. This revealed that granite could be drilled three to four times faster in 10-° molar aqueous DTAB than in water, and confirmed by experiment the suggestion that granite is most effectively drilled with a diamond core bit in environments which impart a zero l-potential to quartz. According to O'Connor and Buchanan' however, the isoelectric point for quartz in aqueous DTAB solutions occurs at a concentration of .•.•2 x 10-° moles per 1, rather than [101 to 10-1] moles per 1. To confirm the results of study I, therefore, a more comprehensive investigation of the [ ]-potentials of quartz, microcline, and Westerly granite in aqueous DTAB environments has now been undertaken. At the same time an examination has been made of one of the basic assumptions of the current conceptual understanding of chemomechanical effects. In this view, although hardness changes occur essentially instantaneously following wetting of the solid, they are confined to a surface layer at most a few micrometers (µm) deep. Hence, to maximize the influence of chemomechanical effects on bit penetration rate only shallow cuts should be taken. Practical penetration rates are then obtained by increasing bit rotation speed. Experimental l-potentials were determined by the streaming potential technique using an automated rapid-cycling apparatus recently developed by Martin Marietta Laboratory from a design by Somasundaran and Kulkarni. The drilling studies employed 3.2-mm-OD 120-grit diamond-loaded core bits with a wall thickness of ~0.7 mm, and bit rotation speeds of 2200 and 25,000 rpm. The load applied to the bit was independent of the depth drilled in both cases. The 2200 rpm measurements employed the same drill press and puddle drilling technique as used in study I. The higher rotation speed was obtained using a water-driven dental turbine drill. In the case, the surface active fluid was pumped down the axis of the bit to ensure efficient wetting and flushing of the drilling debris from the hole. In both cases drilling rate was measured by the parameter D(200), defined as the average rate of bit penetration during the interval from 150 to 250 sec after drilling commenced.

Jan 1, 1976

By E. E. Donath

THE coal hydrogenation process is well known as a means for the production of liquid fuels -from coal. In this paper the possibilities of the coal hydrogenation process as a source of chemical raw materials will be discussed. The recovery of chemicals from coal hydrogenation products necessitates some modifications and additions to the equipment used for the production of fuels. The conversion of coal into liquid fuels such as gasoline requires two steps: liquid phase and vapor phase hydrogenation. Intermediate oils obtained in the liquid phase contain oxygen and nitrogen compounds, especially aromatic compounds, since the coal itself is composed mainly of cyclic compounds. These oils are the raw material for the separation of high molecular weight aromatics and of tar acids and tar bases. The relative amounts of heavy and middle oil-boiling above and below, e.g., 325°C-can be influenced by temperature, residence time, and catalyst of the liquid phase hydrogenation. In the vapor phase hydrogenation a solid bed catalyst is used to convert the intermediate oil from the liquid phase operation into hydrocarbons of the gasoline boiling range. Essentially pure hydrocarbons with a low content of sulphur, oxygen, nitrogen, and olefines are obtained. Depending mainly on the catalyst, the high ring compound content of the liquid phase oil can be preserved and gasoline rich in aromatics obtained. However, with other catalysts, these ring compounds can be split into gasoline with a high content of isoparaffins.1 Again, depending on the operating conditions, products of varying boiling range can be obtained. Selection of catalyst and operating conditions therefore makes possible the production of different grades of motor fuel and also variations in the relative amounts of benzene, toluene, and xylene when aromatic hydrocarbons are produced. The schematic flowsheet, Fig. 1, shows the main steps of the coal hydrogenation process, and the product streams used for the recovery of chemicals are indicated. In the liquid phase hydrogenation stage, coal is made into a paste with recycle heavy oil. The coal paste is mixed with hydrogen and preheated at a pressure of 300 to 700 atm in heat exchangers and preheaters. The coal paste and hydro¬gen enter high pressure converters where the liquefaction of coal, conversion of the high boiling liquid materials initially obtained, into intermediate oils is performed at a temperature around 470°C. The reaction products enter the hot catchpot in which lower boiling oil vapors are separated from the residue containing unreacted coal, ash, and heavy oil. This residue, usually called H.O.L.D. (heavy oil let down), is processed to separate solid and liquid material. By thermal treatment of the residue, e.g., a coking process, distillate oil is obtained, which can be recycled as part of the pasting oil. This stream is rich in polynuclear aromatics and can be, and has been, used for the recovery of such material. The oil vapors and hydrogen from the hot catch-pot are cooled in heat exchangers and a cooler, and the condensed oil is separated from the recycle hy-

Jan 1, 1952

By P. S. Martin, B. J. Guarnera

As an energy source, lignite is short on selling points-it contains large amounts of moisture and often large amounts of ash, resulting in low heat content. The moisture produces rapid oxidation upon exposure and self-ignition commonly occurs within two to three weeks, resulting in major transportation and storage problems. Nevertheless, as interest in alternate fuel sources increases, lignite deposits in the Coastal Plain of the US are attracting more and more attention. Two lignite mines are operating in Texas and additional developments are planned in that state, Arkansas, and Louisiana. At present, Texas lignite is burned only at mine-mouth generating facilities, but more exotic uses such as gasification are projected in the future.

Jan 4, 1979

By W. A. Vine

When a hole is made in a stressed solid, such as rock pierced by mine openings, equilibrium of the solid is destroyed. To restablish that equilibrium the stress condition in the rock surrounding the opening becomes rearranged. This rearrangement may or may not develop local stresses in the vicinity of the opening which exceed the elastic strength of the rock. Since stability of the opening depends, therefore, on the strength of the naturally occurring rock surrounding the opening, this rock is an engineering material of construction, and all rock affected by the associated opening or system of openings may be considered a structure. The term invert is chosen to describe the formation of the structure built from the inside, as it were, and a consequence of mining rather than an entity built for a purpose. By definition, an invert structure is formed when openings are made underground and is com- posed of that material on the solid side of a rock-air interface wherein the stress condition is affected by the associated opening or system of openings. The shape of an invert structure is never clearly defined; the skin of the structure may be mapped, and even described, but the boundary of the structure within the solid rock mass must be arbitrarily set.

Nov 1, 1955

By A. Brown

RAPIDLY rising world demand for mineral pro- ducts has accelerated depletion of the more readily accessible ores, particularly those of premium grade. Operations must proceed at a faster rate to deeper horizons, where there are problems of ground control that restrict economic recovery of the mineral and introduce new hazards to mine personnel. For some of the new Canadian mining fields severe problems of ground stress are still in the future, but much of Canada's mineral output comes from well established mines that have reached considerable depths. It must also be anticipated that the depletion of premium grade ores will eventually necessitate mining low grade material at competitive cost, and unsolved problems of ground control can materially increase costs. Studies of ground stress phenomena in underground workings are therefore considered a present-day necessity, especially since these investigations must be a long-term effort owing to the highly complex nature of the problem and the difficulty of making full-scale observations.

Jan 8, 1958

By C. S. Corbett

There is much comment at present in the ranks of the oil industry regarding unit operation of oil fields and the benefit that would accrue if it could be extensively applied. It seems certain that, as an immediate corrective of the present situation, overproduction could be effectively curtailed with all the advantages of proper conservation of petroleum resources and with no important loss to anyone connected with the industry. Unit Operation in Certain Foreign Fields Many an oil operator in America would doubtless like to have exclusive control of one or more oil-bearing structures for development in accordance with the economic position of the industry and especially in accordance with the best production practice known. A few operators now have this privilege, particularly in certain foreign fields, and are following lines of procedure which show that they are aware of the great opportunity that is theirs. We find in an article by Professor Strigeoff,1 and in a paper read by Captain Comins2 before the American Petroleum Institute, the outlines of procedure adopted, respectively, by the Soviet Government for the nationalized Russian oil fields and by the Anglo-Persian Oil Co. for its fields in Persia. Comprehensive plans for the unit operation of other oil fields may have been described publicly but no such descriptions have come to the attention of the writer. New fields are coming more and more into the hands of single operators or of a few who control large activities and who appreciate fully the need for cooperative action and are willing to forego the lure of a large quick profit from high flush production in order to secure the advantage of better stabilization in the industry and a larger though more deferred profit by operating the field as a unit. Much can be done toward efficient development of an oil field controlled by a few operators who are willing to cooperate for that purpose, but the best result can be obtained only by pooling their interests in the field

Jan 1, 1930

By G. Herget

Finite-element analysis of slopes and a field trial of a slope support system have shown that a considerable potential for excavation reduction exists if slopes are designed with variable slope angles with depth, and if artificial support systems are made an integral part of the slope design. A cost analysis has shown that the savings for a straight 500 ft. high slope with artificial support can amount up to $900 per foot of horizontal pit extension. Horizontal stresses and displacements can be overestimated by up to 100% by employing a two-dimensional finite-element analysis instead of a three-dimensional one. Stress magnitudes differ considerably when comparing results from slope models subjected to a gravity stress field with slope models subjected to high horizontal stresses. Because the latter case appears to be predominant for open pits, slope stability analyses have to be adjusted accordingly. A field trial measuring peak accelerations and displacements has shown that the use of pre- shearing for termination bench blasts, in cases of already heavily fractured ground, can be more detrimental than beneficial.

Jan 1, 1972

By D. R. Skidmore, C. J. Konya

To quantify the effects of proper stemming on air-blast and flyrock reduction for a surface mining operation, a study was undertaken with funding from the Office of Surface Mining. Known weights of explosive charges were detonated in a simulated blasthole when confined with various types and size distributions of stemming. Results showed that proper selection of material type and size distribution can reduce necessary stemming length by 41 % and airblast levels by 23%. A relationship was obtained for minimum length of stemming for explosive confinement as a function of stemming size distribution and borehole diameter over a range of explosive pressures.

Jan 1, 1984

By C. H. P. Lupis, R. Hocine, G. Bernard

The necessary and sufficient conditions for the stability of a multicomponent phase with respect to infinitesinzal fluctuations are derived and transformed to be written in terms of activity coeffcients and mole fractions rather than in terms of the customary second deritlatives of the free energy. NECESSARY conditions for the stability of a multi-component system were derived by Gibbs as early as 1876.' However, as the usefulness of these conditions is greatly enhanced by the simplicity of their translation in terms of functions of common usage, the present contribution establishes these conditions in terms of activities or activity coefficients-and mole fractions. It was shown in another article2 that not only may these conditions be used for the prediction of the appearance of new phases, but they may also provide a check on the orders of magnitude of the interaction coefficients involved. "Spinodal" decomposition is said to occur when, at constant temperature and pressure, the system is unstable with respect to infinitesimal fluctuations in composition. As a result, the "phases" which appear may be attained through continuous changes in the system rather than discontinuous ones, and, consequently, the free energy of these phases may be described by a unique continuous free-energy function. For a binary system, the familiar curve of Fig. 1 illustrates the case we wish to extend to a multicom-ponent system. The conditions to be written pertain to the decomposition of a system of n moles into moles of phase moles of phase v, ...hen moles of phase 9, where the phases a, ...v, ...9 are—at least initially-arbitrarily close in composition to that of the original phase. Each A, is positive and since the total number of moles n in the system remains constant: Each phase v contains hv(nl +dnY) moles of component (I), ...xV(ni +dny) of component + dnk) moles of component (m). The total number of moles ni in the system remaining also constant, it is clear that:

Jan 1, 1968