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By W. E. C. Eustis

During the last year I had occasion, on behalf of our New York copper works, to send to various chemists samples, intended to he accurate, of material which we were buying and selling, and I was astonished to find what differences were reported. After talking over the probable reasons for this with a number of chemists and metallurgists, it was suggested that it would be of real use and some scientific interest to send samples to the different chemists, and take such care in making up the samples that we could feel sure that each chemist had as nearly identical a sample as it was possible to make. After some consideration it was determined to send a mixture which should carry about 50 per cent. copper, and

Jan 1, 1883

By Rixford A. Beals

Dry grinding without balls is feature of this mill now in use in three countries on two continents. Materials being ground commercially include iron ore, gold ore, asbestos rock, and slag. New large beneficiation plants have been using an almost standardized crushing and grinding flowsheet. Typically a primary gyratory is followed by several stages of fine crushing and grinding is often carried out in a rod mill operating ahead of one or more ball mills. The clearly labeled trend is to an increasing number of stages with a decreased reduction ratio per machine. Current Aerofall mill installations represent a complete reversal of this trend-one mill replaces the several stages of crushing and grinding a more conventional flowsheet would call for.

Sep 1, 1955

By Gordon C. Rausser, Michael D. Boehlje, Richard A. Levins, John A. Otte

Changes in SO2 emission standards will not only influence the cost of supplying energy demands from coal, but also the competitive position of various production regions and the method of mining (surface vs. underground). A multiperiod interregional competition model was utilized to evaluate the interactions between mining capacity, new mine development, coal reserves, mining, processing and transportation costs and equipment availability and SO2 emission standards. The empirical results indicate that not only will costs increase dramatically, but production in eastern as well as western regions that have low sulfur reserves will also increase as sulfur standards become increasingly more strict. Implications of the adjustments in the location of coal mining activity for the processing, transportation, and capital goods markets are also presented.

Jan 1, 1978

By Thomas N. Williamson, Victor Zeni

A 6-ft diam core drilling machine has successfully completed seven mine shafts in Virginia and West Virginia to depths as great as 465 ft. There is no practical depth limitation to this new system-a potential method in formations not easily penetrated with other large-scale drilling programs-and higher penetration rates and larger diameters are possible in some formations already being drilled successfully by other methods. The core barrel on the machine is fitted with rolling cutters such as those used on oil field rotary bits, so that less torque is required than with other large- scale drilling systems. The core is made with a wider kerf than is achieved with other coring methods, providing more working room for core drilling.

Jan 4, 1957

By Howard S. Strouth

Investors and mining companies in the U. S. have recently shown increased interest in the Union of South Africa. This has been sparked partially by the founding in the U. S. of a large investment trust which will hold substantial shares in many of the leading gold and uranium producers. The average U. S, mining man's judgment of the Union, however, may be somewhat clouded by recent headline news. We are inclined to take a strong dislike to the stern measures of the present Union government with regard to its native majority. Others possibly think of South Africa in krms of a British colony which, under pressure of rising African nationalism, must eventually be abandoned. These concepts frequently suffer for lack of precise information.

Jan 5, 1959

By Francis S. Kendorski

Caving offers the lowest cost per ton of ally large-scale mining method, but its successful application demands an ore body that conforms to several rigid requirements. The deposit must be of wide areal extent, massive and not spotty in ore values, and insensitive to ore dilution. It must also be a rock mass that breaks up readily. There are only three active caving operations in the US-Climax, Henderson, and San Manuel-but caving methods have recently-taken on new importance as deeper, lower grade mineral occurrences and ore bodies are found. These deposits are too deep for surface mining methods, and too low grade to support any type of underground mining except a bulk method such as caving.

Jan 6, 1978

By Carl H. Schmuck

The terms "cable bolting," "extended ground support," and "grouted cable" are synonymous, and they have been popping up with much more regularity in the mining engineer s vocabulary. In simplest terms, lengths of u itensioned cable up to 18.3 m (60 ft) are grouted in drill holes prior to mining. This permits radical departures from mining practices that rely on conventional rock reinforcement. For example, by placing a pattern of cable bolts in the back of an open stope, ore can be mined in successive slices. After each slice is taken the protruding cable; are simply cut off and mining proceeds. When about 4.6 m (15 ft) of reinforced back remains, a crew places a new par tern of cable bolts in the ore.

Jan 12, 1979

By H. B. Pulsifer

ABOUT 15 varieties, or modifications, of the best magnesium available were prepared and subjected to etching tests, then examined for microstructure. Of the 30-odd etching reagents that were tried, nearly half, mostly ammonium salts, etched the metal satisfactorily. The surfacing and etching of magnesium is shown to be a very simple and quick operation. The density and hardness of magnesium were determined. The most interesting new observations relate to the finding of the hexagonal etch figures, the crystal laminations, and the fact that the metal is plastic, cold, when restrained or quickly deformed. Under slowly applied pressure cold metal deforms slightly, then shears to fracture without plastic flow: The chief structural features of magnesium are presented in two reduced photographs and 30 photomicrographs.

Jan 1, 1927

By R. L. Loofbourow, Roger V. Pierce

THE degree to which our mineral requirements are being met by mining leaner, more complex or more remote deposits is indicated by developments during 1953. Heavy capital investment, skilled technical advice, planning, and able execution are requirements for the typical venture. Producers, faced with rising costs and with softer prices, are seeking improved mining and recovery. Developments in production of iron ore are typical of the course being followed in metal and nonmetal mining. Iron ore development in the U. S. is concentrated on the spectacular work with Lake Superior taconite, while in Canada new production is expected from Labrador and output from Steep Rock, Algoma, and Newfoundland is being increased. Shipment of iron will soon be made from Venezuela.

Jan 2, 1954

By Louis E. Toth, Alan W. Searcy

A modification of Le Claire's microscopic model for self-diffusion is developed in a form suitable for prediction of activation energies for diffusion in disordered substitutional solutions as well as in pure metals Bonding is considered as a localized interaction, and the energy of bonding between atoms of different types is taken as the arithmetic mean of the energies in the pure elements. The activation energies for vacancy formation and migration in substitutional alloys are shown to depend on the empirical constants developed for self-diffusion when the equations are adjusted for the mole fractions of the two elements. The differences in activation energies between alloys and pure metals are calculated and compared with the experimental differences. MaNY different correlations have been proposed for use in predicting activation energies for self-diffusion or diffusion in dilute alloys. Usually theories for self-diffusion cannot be applied to alloys nor can theories for dilute alloys be satisfactorily adapted to self-diffusion. We present here a correlation scheme which can approximate activation energies for diffusion, vacancy formation, and atom migration in substitutional-alloy systems of any concentration. The activation energy for self-diffusion QD has been correlated to the melting temperature Tm,1, 2 the sublimation energy L,,l the heat of fusion Lf,3 crystal structure, and valence.4 Working with mechanical parameters Le claire5 proposed that the activation energy for vacancy migration Qm could be related to appropriate shear moduli. He also proposed that the activation energy for vacancy formation 62, is proportional to Ls. THEORY We consider that Le Claire's expression for 4, is satisfactory. But an alternate expression for Qm in terms of the bulk modulus is just as satisfactory from a theoretical point of view for the prediction of the energy of vacancy migration in pure metals and can more easily be used for alloys. In order for Qm to be a minimum, not only the moving atom but also adjacent and nearby atoms must undergo distortions. These distortions are neither isotropic as is implied by a correlation with the bulk modulus nor unidirectional as implied by a correlation with a shear modulus, but are complex and multidirectional. A complete analysis in terms of the bulk modulus and all the shear moduli is not yet available. In a first approximation in which only one parameter is used, there is no obvious theoretical reason to prefer the shear modulus over the bulk modulus. The bulk modulus is a much more convenient parameter for use in predicting Qm. Shear moduli are known for less than half of the metallic elements while bulk moduli are usually available. Furthermore, because of the directional dependence of shear moduli, their estimation for alloys appears inherently more difficult than is the estimation of bulk moduli. We assume that the bulk modulus Bs reflects an average value of the shear moduli such that the strain energy at the point of maximum distortion of the lattice during vacancy migration can be expressed as

Jan 1, 1964

By Erwin Pink

It has been pointed out in a previous publication' that, for a given strain rate, serrated yielding can be observed only at certain test temperatures. Fig. 1 shows the results obtained for polycrystalline and re-crystallized tantalum, Va group in the periodic table of elements, where serrations in the course of deformation match the decrease of total elongation. However, there was no evidence of repeated yielding when testing molybdenum or tungsten, VIa group, at similar conditions, i.e., annealed and air-cooled samples (serrations have been found in quenched tungsten2). The reason for the observed serrations in the stress-strain curve are dissolved impurities on interstitial sites of the lattice. Of importance is the concentration of oxygen, carbon, and nitrogen, which are in random solution. Two methods to calculate the limiting concentrations for serrated yielding have been evaluated and applied with more or less success in estimating the role of carbon and nitrogen in mild steel.3 J. Friedel4 has given two equations, which determine the upper and lower strain rates i for the appearance of serrations at a certain test temperature: W denotes the binding energy of the interstitial atom, -1 ev for refractory metals;5 e' the portion of continuous strain in the discontinuous stress-strain curve, measured as -3x10-3; b the Burgers vector, c the concentration, see Table 11, in atom fractions; p the dislocation density, -2 X l09 per cm2 at an average stress ?, -15 kp per mm2 at medium strain. k stands for the Boltzmann constant, T for the absolute temperature, and D for the diffusion coefficient. Table I. Eq. [1], for a given strain rate, determines the minimum temperature, and [2] the maximum temperature, below or above which no "dynamic strain-aging" can occur. According to the calculation, which uses the given quantities, serrations should only be observed within the cross-hatched temperature regions in Fig. 1, and this is in good agreement with the experiment. The effect of varying impurity concentrations is indicated schematically in Fig. 2: only Eq. [I] is affected. Setting Eq. [I] equal to [2], one can calculate the limiting concentration cmin which first causes serrations. The second method uses the aging condition by Cottrell and Bilby6,7 \£i/ \ n. a / where n(t) is the number of impurity atoms, which segregate at a dislocation line of 1 cm length after the time t (t in our case is the time between "repeated yield drops" in the serrated curve, or, the time until the above mentioned strain E' is obtained, i.e., -1 sec for medium intensity or serrations). no is the number of impurity atoms in 1 cm3 and A = Qb4ep[(1 + v)/(l - v)], derived from equations given in Ref. 7. p is the shear modulus, 18,800 kp per mm2 for tantalum, 12,200 for molybdenum, AE the tetragonal distortion caused by interstitial impurities in a bcc lattice (approximately 0.4 for both tantalum and molybdenum) and v Poisson's ratio (0.35 for tantalum, 0.30 for molybdenum). From Eq. [3], combined with the condition for a pronounced yield drop as formulated by cottrel16 (at least one impurity atom segregated at the unit length of a dislocation), again a no min, and hence the concentration Cmin can be calculated.

Jan 1, 1970

By J. M. Campbell, T. S. Buxton

The most widely used methods of predicting the volumetric properties of gas are based on the principle of corresponding states, which asserts that the compressibility factor is a universal function of reduced temperature and pressure. Previous studies have shown that the acentric factor, as proposed by Pitzer, l is an important addition to reduced pressure and reduced temperature as factors affecting the compressibility factor. Results of this study indicate that, if the pseudocritical temperature and pressure used to determine the reduced conditions are adequately predicted, characterization of natural gas-carbon dioxide mixtures with the acentric factor will allow reliable determination of the compressibility factor. Comparisons of predicted and experimental compressibility factors have shown that the pseudo-critical constant rules of Stewart, Burkhardt and Voo 2 are satisfactory for hydrocarbon mixtures. However, these rules fail to predict the pseduo-critical constants for hydrocarbon-carbon dioxide mixtures. Based on graphically determined pseudocritical temperatures for binary hydrocarbon-carbon dioxide mixtures, a correlation which gives the required correction to the Stewart, Burkhardt and Voo rules was prepared and a compressibility factor prediction technique was proposed. To test the proposed technique, compressibility factors for live mixtures of methane, carbon dioxide and either ethne or propane were experimentally determined at 100, 130 and 160F and pressures up to 7,026 psia. The predicted and experimental compressibility factors for these live mixtures had an average absolute deviation of 0.55 percent. INTRODUCTION Two-parameter generalized correlations based on the principle of corresponding states (PCS) are presently available for reliably predicting the compressibility factor of lean natural gas, i.e., natural gas with low concentrations of hydrocarbons heavier than methane. When these same correlations are used for mixtures of natural gas and carbon dioxide, large deviations between actual and predicted compressibility factors are observed. This study was undertaken to provide a means for accurately predicting the compressibility factor for such mixtures. In the past, two avenues of approach have been employed to extend the applicability of the PCS. The first has been to introduce additional parameters. The second has been to develop combination rules for predicting pseudocritical constants which do not suffer from the limitations of the commonly used molal average constants. In this study, both of these approaches have been considered and employed to arrive at a method for predicting the compressibility factor of mixtures of hydrocarbons and carbon dioxide. SELECTION OF A THIRD PARAMETER Failure of the original PCS to predict the compressibility factor for all pure gases, regardless of their mass, shape or polar moment, has led to the introduction of additional parameters into the PCS. Parameters have been introduced to correct for quantum deviations,3-5 non-spherical or globular shapes6-9 and for polar moments.8-12 In addition to these parameters which are based on some microscopic property and intended to correct for some specific cause of deviation, more general parameters based on some bulk property have also been introduced.1913-16 To use additional parameters to correct for each of the possible causes of deviation among the individual constituents of a gas mixture would require a rather complex form of the PCS. To maintain the PCS in as simple a form as possible, it is more desirable to have a single third parameter which is based on some bulk property influenced by several of the factors causing deviations. The third parameter selected for use in this study is a factor originally proposed by Pitzer.9

By A. C. Emery

The physical and chemical properties for the metalliferrous feed materials to the Imperial Smelting Process blast furnace are defined and the means of achieving these properties by the sintering or briquetting routes discussed. Modern sinter plant performance data is included with a plant flow sheet showing draughting patterns. The necessity for ensuring an adequate SO2 content in sinter machine gases when roasting sulphide materials to enable conversion to sulphuric acid in a contact acid plant is described. The ability of the process to consume limited quantities of oxide materials, residues from other processes and other secondary sources is discussed. The argument for a briquetting route is developed out of this limitation and the merits of cold and hot briquetting examined. Development work on the hot briquetting route for this purpose is briefly described and several flow sheets outlining possible applications for hot briquetting to different raw material situations including the preparation of low lead charges for the furnace are presented.

Jan 1, 1977

By E. D. Glass, R. C. Hessing

The volume of gas in storage reservoirs may be compuled from estimates of hydrocarbon pore volume and gas density. However, both are dificult 10 estimate accurrately. Further, no adequate method has been presented for estimating reservoir performance during operation for Volumetric gas-storage reservoirs. Normally, gas-storage reservoirs exhibit small pressure gradients in the area conr(zilliitg the storage wells, even under conditions of maximum injection or withdrawal. A zone of low permeability usally surrounds, and is in communication with, tile permeable zone which causes the storage reservoir to exhibit a definite pressure lag, as evidenced by lack of pressure stabilization after extended periods of shut-in. An analysis is presented for determining pore volume and gas in place, and for predicting future reservoir behavior of such reservoirs. The mathematical development is presented and a solution is shown for an operating storage reservoir. INTRODUCTION Depleted gas reservoirs arc often used for gas storage. The reservoir usually contains a permeable area in which numerous storage wells arc located. The permeable zone permits high deliverability and injectivity with relatively small pressure loss. However, pressure equilibrium may not be attained even after long periods of shut-in because of the fact that the permeable zone is in communication with an adjacent tight section. Most of these gas-storage reservoirs are sand lenses, such as ancient beaches or offshore bars. The areal geometry of these reservoirs is normally such that flow in the tight zone will be approximately linear, and the solutions presented here should apply. DISCUSSION For purposes of this paper, a gas-storage reservoir is considered to consist of a volume of permeable rock in communication with tight rock, all of which is surrounded by an impermeable barrier. Pressure gradients across the permeable zone are small due to low flow resistance and well density. Hence, the permeable zone is considered to be at a uniform pressure which is only a function of time as gas is injected or withdrawn. The tight zone is considered to be linear with uniform permeability and porosity, and the pressure in the tight zone is a function of both position and time. l'wo solutions for flow in this system are used to define the reservoir and determine its properties. The first solution is for an infinite linear tight zone in communication with the permeable zone. The expression for constant gas-withdrawal rate is Eqs. I and 2 ore superposed to account for varying rates of production or injection and are used to fit gas-storage field reservoir history. The solution for the infinite case, Eq. 1, is first applied to field data for early times following a shut-in period. Constants BDa and c are ohtained by a least-squares fit of pressure and rate data. After the pressure wave from gas injection or withdrawal reaches the external boundary of the tight zone, the infinite solution will no longer apply and pressure behavior should be more nearly represented by Eq. 2 for a gas reservoir in communication with a finite linear tight zone. The values of the constants found from curve-fitting Eq. 1 to the early time data may then be used in Eq. 2 that only the coefficient- L containing the unknown

By J. B. Conway

RECENT studies of first-stage creep data have led to a special least-squares procedure for use in calculating the Andrade creep-equation constants. This procedure is easy to apply, uses only experimental data, and yields results which do not vary with the individual making the analysis. Taking logarithms of the Andrade equation I = lo(1 +ßl1/3)ekt leads to In l = In lo + In(1 + ßl1/3) + kt A residual can then be defined as the difference between the logarithm of an experimental length value and the logarithm of a calculated length value. Following the usual least-squares approach differentiation with respect to 10 and k of the expression for the sum of the squares of the residuals leads to two equations which cannot be solved directly for the three constants involved. However, values of ß can be assumed and corresponding values of lo and k can then be calculated. Then the sum of the squares of the residuals can be calculated. For a certain value of ß this sum will exhibit a minimum value to identify the least-squares values for ß, lo, and k. An illustration of the application of the above least-squares approach is obtained by employing the creep data for lead originally presented by Andrade' in the development of the one-third creep law. A plot of the sum of the squares of the residuals as a function of ß is shown in Fig. 1 along with the corresponding lo and k values. The minimum is seen to occur at ß = 0.0143 from which lo = 39.149 and k = 7.27 x 10-5. Based on these results the Andrade equation for these lead data is 1 = 39.149(1 + 0.0143 t1/3)e7.27 x 10-5t compared to the equation I = 39.13(1 + 0.01457/l/3)e6.95 X 10-5t developed by Andrade (calculation procedure not given but was probably a graphical solution). Calculating length values using the above equations and comparing with the experimental length values, residuals corresponding to the difference between experimental and calculated length values can be obtained. The sum of the squares of the residuals can then be calculated. For the case of the least-squares approach a value for this sum was found to be 2.37 x 10-3 compared to a value of 3.47 x 10" for the equation originally proposed by Andrade. In other words, while the constants proposed by Andrade provide an excellent fit for the lead data, a still better representation is afforded by applying the least-squares approach discussed above. A similar result was obtained for the lead data at 162oc.l The least-squares approach led to 1 = 9.866(1 + 0.0497 t1/3)el.011 x 10-2t compared to the equation I = 9.94(1 + 0.0433 l1/3)e1.06 X 10-2t given by Andrade. In this case, too, the sum of the squares of the residuals is slightly smaller for the equation based on the least-squares approach. It should be pointed out that a double trial and er-

Jan 1, 1965

By E. F. Sumner, C. K. Eilerts

A partial differential equation was developed and programmed to compute the cumulation and flow of the liquid phase of a gas-condensate fluid. It was found that such cumulation near the wellbore may attain saturations permitting liquid flow within periods of the order of 1 day. The radius at which this saturation obtains advances toward the external reservoir boundary with continued recovery, although it may move only 2 to 5 percent of that distance during the productive life of the well. This relatively high saturation can cause a serious dimunition in delivery capacity. The pressure dilferential required for flow of gas through a formation with such saturation may be as much as three times greater than the corresponding differential in a formation where saturation is less than 2 percent. Because of the radial geometry, total reservoir pressure differential required for flow with a zone of relatively high liquid saturation about the well was indicated to be two to three times greater than without the saturation. INTRODUCTION A computing program developed by the authors 1 to integrate the partial differential equation for transient radial flow of gas-condensate fluids required a prevalued function, W(Po) = kD(p0)/M(p0)z0(Po).......(1) related to cumulation of condensate in pores of the reservoir as pressure declines. Methods were available for relating mobility to saturation, saturation to liquid-vapor volume ratio, liquid-vapor volume ratio to pressure and, hence, mobility to pressure to obtain W(pD). However, certain assumptions had to be made in advance of program execution concerning movement of the liquid phase and change in radial distribution of liquid saturation as recovery progressed. Because reservoir fluid mobility and related pressure gradients are markedly dependent on liquid saturation, it was desirable to eliminate the necessity for these assumptions and in this respect improve the reliability of a result obtained by integration. Experimental research was begun to determine the relationship of variables that control the reservoir flow of low liquid-vapor ratio fluids. With the porous medium partly saturated, permeability to a two-phase flowing fluid could not be measured because the viscosity was unknown. Viscosity could not be measured without knowing permeability of the liquid-containing medium; but mobility, the ratio of permeability to viscosity, was measurable. This property, and liquid-vapor volume ratio of the flowing phases, have values determined by nature of the fluid and porous medium and, in addition, were found to be pressure, velocity and saturation dependent. A program developed by Kniazeff and Naville 2 for computing multicom-ponent, two-phase flow used polynomials to represent saturation dependence of permeabilities for gas and for liquid phases, and an effluent viscosity constant under reservoir conditions. The authors developed a program based on a partial differential equation of similar mass balance origin but designed to represent distribution of an unlimited number of components between gas and liquid phases utilizing the experimental information available as to variable dependence. Attention was given to liquid-vapor volume ratio of the flowing phases, a property which is essential as a liquid saturation boundary condition. A program for computing implicitly saturation increase at uniform intervals along the drainage radius was combined with an existing program for calculating pressures, and the two were used alternately in an iterative solution for both saturations and pressures. The function W(pD) needed for calculating pressures was replaced by the ratio of mobility to compressibility factor. BASIC EQUATIONS The partial differential equation for calculating

By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

Apparatus and a method for determining the volumetric behavior of hydrocarbons at pressures up to 10,000 psia and at temperatures between 0° and 460°F are described. The equipment is suitable for measuring the total volume of the system and the volume of a liquid phase as functions of state within these ranges of temperature and pressure. Introduction During the past two decades there has been a marked increase in the ranges of temperature and pressure encountered in underground hydrocarbon reservoirs of commercial interest. In addition, greater interest in the intensive characteristics of the fluids found in these reservoirs has developed. Apparatus Several types of apparatus have been developed in the authors' laboratory for volumetric measurements of hydrocarbon systems. The earliest equipment described1 was characterized by constant volume, and the weight of material present was varied systematically in order to attain the different pressures desired in the study. Later another apparatus2 was built in which the effective volume of the cylindrical cell, which confined a hydrocarbon sample of constant weight was varied by injection or withdrawal of mercury. The effective total volume of the equilibrium cell was measured by ascertaining the position of the mercury surface but no measurement could be made which gave knowledge of the volumes of individual phases existing within the hydrocarbon system. A third apparatus3 was designed for use at higher pressures and temperatures than the earlier equipment would tolerate. This apparatus was of the variable volume type but was built in the general form of a U-tube, the mercury level being measured at the surface which was not exposed to the hydrocarbon system. This arrangement avoided the need of subjecting measuring equipment to the extremes of temperature at which studies were made, but it gave no provision for measurement of the volumes of individual phases. Although this last apparatus was satisfactory as to accuracy and convenience for many purposes, need was felt for measurements of the volume of the liquid phase of the hydrocarbon system. For this reason a fourth equilibrium apparatus was designed and constructed, and it is the purpose of the present paper to describe it. The equilibrium cell has a working range of temperature from 0° to 460°F at pressures up to 10,000 psi. Provision for measurement of both total volume and liquid-phase volume makes it particularly suitable for the equilibrium study of heterogeneous systems consisting either of simple mixtures or of complex field samples of hydrocarbons. The general arrangement of the ap-

Jan 1, 1948

Apparatus and a method for determining the volumetric behavior of hydrocarbons at pressures up to 10,000 psia and at temperatures between 0° and 460°F are described. The equipment is suitable for measuring the total volume of the system and the volume of a liquid phase as functions of state within these ranges of temperature and pressure. Introduction During the past two decades there has been a marked increase in the ranges of temperature and pressure encountered in underground hydrocarbon reservoirs of commercial interest. In addition, greater interest in the intensive characteristics of the fluids found in these reservoirs has developed. Apparatus Several types of apparatus have been developed in the authors' laboratory for volumetric measurements of hydrocarbon systems. The earliest equipment described1 was characterized by constant volume, and the weight of material present was varied systematically in order to attain the different pressures desired in the study. Later another apparatus2 was built in which the effective volume of the cylindrical cell, which confined a hydrocarbon sample of constant weight was varied by injection or withdrawal of mercury. The effective total volume of the equilibrium cell was measured by ascertaining the position of the mercury surface but no measurement could be made which gave knowledge of the volumes of individual phases existing within the hydrocarbon system. A third apparatus3 was designed for use at higher pressures and temperatures than the earlier equipment would tolerate. This apparatus was of the variable volume type but was built in the general form of a U-tube, the mercury level being measured at the surface which was not exposed to the hydrocarbon system. This arrangement avoided the need of subjecting measuring equipment to the extremes of temperature at which studies were made, but it gave no provision for measurement of the volumes of individual phases. Although this last apparatus was satisfactory as to accuracy and convenience for many purposes, need was felt for measurements of the volume of the liquid phase of the hydrocarbon system. For this reason a fourth equilibrium apparatus was designed and constructed, and it is the purpose of the present paper to describe it. The equilibrium cell has a working range of temperature from 0° to 460°F at pressures up to 10,000 psi. Provision for measurement of both total volume and liquid-phase volume makes it particularly suitable for the equilibrium study of heterogeneous systems consisting either of simple mixtures or of complex field samples of hydrocarbons. The general arrangement of the ap-

Jan 1, 1948

By Leigh J. Wardle

SUMMARY This paper describes a numerical method for calculating the three- dimensional stresses and displacements induced by tabular excavations in a rock mass consisting of parallel layers of distinct material properties. The method is based on the superposition of numerical solutions for elementary displacement discontinuities in a parallel layered rock mass. The method can be used to analyse complicated excavation layouts such as those encountered in room-and-pillar or longwall mining. The method can automatically take into account the effect of the earth's surface. The method offers an economic and efficient solution to stress analysis problems which cannot be adequately modelled using two- dimensional methods and for which the expense of three-dimensional finite element or general boundary element analysis cannot be justified. INTRODUCTION Underground mining often takes place in tabular or lenticular orebodies. In many cases, for example room-and-pillar and longwall mining, the excavation geometry cannot be adequately modelled by two- dimensional methods of analysis. In these cases resort must be made to three-dimensional methods of analysis. Although in principle three-dimensional finite element models can be used for these geometries, cost limitations have restricted their application to a small number of cases. For example, room-and-pillar systems of regular pattern have been analysed by numerically modelling

Jan 1, 1984