Search Documents

By George Bain

SOME problems concomitant with commercial exploitation of marble are presented as examples of interesting, useful and profitable fields for application of scientific knowledge. The marble industry is only one such field and is selected because its varying new aspects are familiar to the author. However, what is true for marble is equally so in principle for many industrial minerals. The problems of any stone industry are to maintain markets, create new outlets for stone already in demand, and develop varied uses for varieties that are not so popular. Here the geologist has a different role from most of his colleagues in metal mining. The producing branch may ask about the expectable variation in thickness or size of a deposit as development proceeds. The stock department may call for the available amount of a given type of stone before accepting a large order. The sales force requires data on the use for stone from certain parts of deposits in order to divert grades to the most suitable use. The service depart-ment wants defects rectified and the cause determined to avoid recurrence. The mills want data on durability and cutting quality of abrasives. The geologist occupies no special department; he is on general call, as may be illustrated by a few types of problems that may be classified as: (1) dominantly geological in character, (2) dominantly chemical in character, (3) dominantly physical in character.

Jan 1, 1940

By B. R. Coil, C. A. Ross

NEW demands for underground power in the Miami mine of the Miami Copper Co., Miami, Ariz. has brought about expansion of the distribution system for both ac and dc power. Progress in mining equipment and the normal changes in the mine were responsible for this increased demand. Early power requirements were for pumping and haulage. A 440 v ac power line down No. 5 shaft took care of a small pumping load and shaft station lighting, 275 v dc power was generated by motor generator sets on the surface, with a churn drill hole from surface to the 570 haulage level serving as a cableway. Electric lights were installed where power was available, and thus were confined to the haulage level and shaft stations. All industrial power in the Miami area is 25-cycle, which dates back to the hydroelectric generator installation at Roosevelt Dam in 1908-10. The Problem The main haulage level was moved to the 720 level and later, to the 1000 level, requiring a longer feeder line with the resultant voltage drop. Also, as mining progressed to the east, the churn drill hole for the power cable would have been subjected to subsidence cracks. The first extension in the use of electricity was in electric blasting. About 1935 the mine went to electric blasting, using the dc haulage current. Bringing electric current to the working levels of the mine for blasting greatly expanded the use of electric lights. Lights were used in tool rooms, powder and cap magazines, stairways, and other semi-permanent installations. Like all mines, Miami Copper began to study and experiment with mechanical mucking and transportation of ore by slushers, shakers, and belts during the late 1930's and early 1940's. At the beginning of the program, power was supplied from the haulage level 275 v dc system. Later it became necessary to run a cable, carrying 440 v ac power, down the No. 7 ventilation shaft. The increased use of power came about gradually, and many new problems were added, not the least being the introduction of switch boards and power cables into the working areas of the mine, where drifts and crosscuts take weight, and require repairs. The 25-cycle current presented special problems, in that 25-cycle transformers are twice as large and about 2V2 times as heavy as 60-cycle transformers of the same power output. The 25-cycle transformers were considered too large for installation in the mining areas. In 1947 the distribution system was revised and standards were adopted, governed by the following

Jan 1, 1952

By G. A. Vissac

O. R. LYONS *—I wish to thank Mr. Vissac for his compliment. I hope that his paper is not only well received, but that it will serve to bring forth more papers on the subject of thermal drying. One of the primary purposes of the work performed by Battelle for Bituminous Coal Research in investigating the thermal drying of coal was to stimulate other investigators and to get them to contribute their knowledge in the form of papers such as this one. We at Battelle and the personnel of Bituminous Coal Research are very gratified that Mr. Vissac and other persons have responded in this matter of the thermal drying of coal. I wish to state that I think that Mr. Vissac's paper is a very clear and easily understood description of a method of calculating the design requirements for a screen type drier, and I think that it would be exceedingly valuable to operators and to those who intend to purchase any type of thermal drier and use it in the future, if the manufacturers or operators who have such information for other types of driers would provide the same type of information for the other makes of driers now on the market. 1 also wish to point out—an idea that is new to me, and I know is new to most of the operators of driers in the United States-—the idea of recovering the heat that is normally lost in the coal and in the exhaust gases. This heat is not being recovered at most (of the thermal drying operations in the United States, and the possibility of recovering it should be called to the attention of every single one of those operators. I know many of them have never given any thought to the matter, but they will be interested once they realize the ease with which it could be done and the savings that could be realized. I also wish to compliment Mr. Vissac for presenting the method of analysis that he uses to determine the difficulty of drying any particular coal. It is a very simple method, and yet it seems to me that it should be a very effective, very efficient method for determining the difficulty of drying for his particular problems. C. Y. HEINER*—I do not know that I can add anything very illuminating to what Mr. Vissac has said. I think anything that Mr. Vissac said in regard to coal drying is a contribution because, to my personal knowledge, he has studied the matter carefully for many years and made many valuable contributions. I am not too familiar with coal drying problems in the east, but I know in the west we have not made enough coal drying studies. I think coal operators too often just take the coal as it is and make more or less the best of it. There are relatively few washing plants in the west now, and so the problem has not come to the front as much as it probably will in the future. In this connection, it seems to me that this matter of drying the raw coal, as Mr. Vissac brings up, is an extremely important one. We have not a continuous miner ourselves, yet, but we expect to get some this year, and we think the percentage of fine coal-—that is, minus 3/16 in.—will double. We have about 20 pct minus 3/16 in. in the 8 in. by 0 size now, and we think we will likely have 40 pct, which will have a surface moisture of the order of 8 pct. To wash it satisfactorily, we will have to dry the raw coal first in order to screen it, and after that, I suppose, there will have to be dry cleaning of some sort. We have not really used dry cleaning on fines in the west yet to my knowledge, but it is a matter that has to be faced by the industry, and I am very hopeful that Mr. Vissac's study will assist us in that connection. W. L. McMORRIS*-In my company we are preparing largely metallurgical coal for a great number of byproduct coke plants. The most outstanding thing to me about the requirements of moisture in the finished product is that there is a different requirement for almost every coke plant. Each operator has a different set of factors on which he establishes his coking costs where they involve moisture. For our corporation operations in Birmingham, my company does not produce the coal, but in Birmingham they are getting away with moistures very much higher than our plant at Clairton, Pa., would tolerate. The moisture that we have to produce for the plants along the lakefront where they are subject to much more severe weather is something else again. We have not tackled heat drying, primarily because our customers do not know what heat drying will do to the coking characteristics of the coal. If the temperature of drying can be held down

Jan 1, 1950

By Jay A. Carpenter

This paper deals with only one step in the treatment of ore at the West End mill; not because the other steps are repetitions of practice in other mills, but because in this particular step there is in use the Trent agitator: This device, although it has apparently failed in many mills, is here giving excellent service and has proved to be well adapted for making a thorough replacement of pregnant solution with a minimum amount of barren solution. The strong and weak points of this agitator, its present simple construction, and its use as a thickener for agitator or battery pulp are features of interest; but perhaps the point of greatest interest to the metallurgist in this day of continuous decantation is its use in a series of tanks for slime treatment by the replacement method. The agitating department of the West End mill consists of six redwood tanks, 24 ft. in diameter, 18 ft. high, each equipped with a Trent agitator, a centrifugal pump, and a motor. The pulp is transferred by a pump from the top of a flat-bottomed tank to a set of arms and nozzles in the bottom of the tank, at just sufficient pressure to cause the arms to revolve. The streams from the many nozzles keep the bottom of the tank clean, and these streams, coupled with the effect of the revolving mechanism and the ascending current, keep the pulp in constant motion and of constant gravity. These agitating tanks hold 90 tons of dry slime and 202 tons of solution with a 1.24 pulp, our ore having a specific gravity of 2.7. This capacity is about 10 per cent. in excess of the standard 15 by 45 ft. Pachuca tank. The tanks are connected in one series for continuous agitation, the pulp for each agitator being drawn by its pump through a branch suction from near the top of the preceding tank and delivered to the bottom of the tank by the agitator arms along with the regular pulp of that agitator. This method works automatically, since the flow through the branch suction varies directly with the difference in head of the two tanks. The chance for new pulp to pass out quickly is, therefore, much less than in many other systems of continuous agitation, since the new

Jan 1, 1916

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

By P. H. Dudley

A quarter of a century of service of steel rails on our oldest railroads, many of which have changed their standard sections three or four times, has furnished, and is furnishing, excellent opportunities to study their wear and behavior in the track. Such experience is valuable for the design of new sections, now required to meet the constantly increasing severity of railroad service. Before presenting the new sections for consideration, I will briefly call attention to some features of past experience. For convenience of study, rails may be separated according to their weight and height into four groups, viz.: 1. Hails weighing per yard from 52 to 60 pounds, and 34 to 4 inches high. 2. " " " " " 60 " 72 " " 46 to 44 " " 3. " " " " " 72 " 90 ' 41/8 to 5 4. " " " " " 85 or more " " over 5 " I Experience in this country is confined mainly to sections in groups Nos. 1, 2 and 3. • During the past few years I have had the opportunity to run my car over many thousands of miles of railway laid with the principal sections in use, and to obtain diagrams showing their deflections, permanent set, and, in a great measure, their manner of wear. The First Group.—The first steel rails imported, and those manufactured here, were light sections—included in the first group—and many of them, being rolled in rolls used for rolling iron sections, have pear-shaped heads, 2 3/8 to 2 1/2 inches wide, the base being heavy and from 1/4 to 1/2 inch narrower than the height. These rails were laid upon ties of solid timber, at least 8 inches face, spaced 2 feet from center to center. The moments of inertia of these rails were low, only ranging from 8 for the lightest sections to 12 for the heaviest. The deflections were, of course, great; but the quality of the metal was excellent. It was physically hard and

Jan 1, 1890

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 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 Rich Akerman

as 1866, I wish to assure both these gentlemen that I had not seen the section when I designed mine, :md even if I had, I should not have then dared to put it forth as a standard for English rail makers; tind the soundness of my opinion has a simple but conclusive proof in the statement made concerning the extra price which was at that time required for their production. I need not say that I highly approve of the original Welch section, for it is in principle similar to the design which I made ufteen yeam subsequently; and from a professional point of view I would fully concecle to Mr. Welch the credit of first designing the modern steel-rail section. From com- mercial, matter of tict, and practical point of view, he was, however, before his time by many years; or to put it in another way, rail making was ten years behind its time when the new metal steel was first introduced for rails. If his design has been incorrectly identified with my name (as the sections are similar in principle, though they differ in thickness of flange and web), I beg to say (1st) that I much regret the misun- Understanding which has arisen through no fault of niine, aud (2d) that no confusion has been intentionally created by me. It is a pity that the section designed so long ago has not been made public at an earlier date, as it would make a really goal stand- and pattern, anil even now be quite equal to present requirements. In conclusion, I wish to say that I have never desired to claim any invention or novelty by the publication of my sections; they Were put forth as being such as English railmakers could and would produce at the ordinary market. price, and as being the best and most suitable to be so obtained. Had Mr. Welch or Mr. Holley put forward theirs ten or fifteen years ago, I should have been the first to recommend theru. In fact I should have been glad to see their narnes associated with rail patterns in their own country, in the same way as mine has been. PROFESSOR RICH. AKERMAN, STOCKHOLM, SWEDEN: i AGREE with your (Mr. Sandberg's) views that it is too early yet to stipulate only one definite chemical composition in the rails. Such a stipulation, I think, might he justified, if it were not for the manganese; but this metal changes the properties of the iron aud steel in tho same direc- tion ae carbon, silicon. and phosphorus, by increasing its tensile strength, stiffness, hardness, and brittleaess. If the iron and steel does not only contain carbon and manganese but also phosphorus,

Jan 1, 1881

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

By R. E. Collins, Paul B. Crawford

Mathematical equations have been derived to show the effect of the slippage phenomomenon (Klinkenberg effect) on unsteady-state gas flow through porous media. The assumption is made that the slippage may be represented by an equation of the type It is pointed out that most of the existing data on unsteady gas flow may be corrected for slippage by a simple change in definition of the dimen-sionless groups. INTRODUCTION Several solutions to the various problems associated with the unsteady-state flow of gas through porous media have been recently presented in the literature.','" The cited publications have resented solutions for flow under ideal conditjons. The principal assumptions involved include: (a) the density of the gas obeys the perfect gas law; (b) the viscosity of the gas is constant; and (c) the gas permeability is constant. Few, if any, actual gases under reservoir conditions are believed to conform with the above, but the ideal solutions do provide the basis for making improved estimates on the performance of gas reservoirs. The purpose of this paper is to show the performance characteristics when assumption (c) is corrected for the slippage phenomenon or the Klinkenberg effect. This is believed to be a step nearer to reality. MATHEMATICAL DEVELOPMENT Case 1. Gas Flow — Ideal Conditions The equations describing the flow of gas under ideal conditions have been clearly presented in the cited literature; however, for completeness of this work they are repeated here. The basic differential equation describing the flow of gas is Equation (6). It may be derived as follows: The continuity equation, the perfect gas law and Darcy's law are combined to give: Manuscript received in the Petroleum Branch office Aug. 3, 1963 or If — is constant, Equation (5) is rewritten to form the basic Equation (6). or for the linear case A dimensionless equation is obtained by dividing through by (pl)z and making the substitutions shown below: The resulting equation is A similar procedure for the radial case leads to the following equations: where and Equations (11), (12), and (13) are those used by Bruce, et al., and Jenkins and Aronofsky for their computational work.

Jan 1, 1953

By Richard Moldenke

So far as the quality of the product is concerned, the history of the production of pig iron for foundry purposes is one of constant retrogression. The steps in this deterioration began with cold-blast charcoal pig iron, then anthracite iron, coke iron; then gradually warm to hot-blast coke iron, with the charcoal furnaces also heating their blast to get greater tonnages, and finally the present-day hot-blast coke irons with scrap additions to the ordinary burden that, according to one European report, have gone as high as 65 per cent. Parallel with this quality retrogression is the enormous increase in furnace tonnages from about 15 to over 1000 tons per day in excep tional instances of modern practice. The key to this situation is economic pressure. The effect is a growing differentiation between furnace production for gray iron and malleable foundries and for the production of commercial steel. As the foundry is often compelled to draw upon the pig irons made for steel purposes, for economic reasons, whereas the steel industry does not draw upon foundry pig irons proper, the situation is resolving itself into one of grave consequence for the life of the gray-iron castings industry, and hence the intensive present-day feeling in foundry circles for rigid specifications to govern the quality of pig irons sold for foundry use. In the discussion of a paper on the use of scrap in the blast furnace held recently in the Institute, a very pertinent remark was made by one of the participating furnacemen, who confessed that "the things found wrong by the foundryman with his iron were beyond his depth." It may be added that those things are also beyond the depth of most foundrymen who, however, know from their results that they are getting poorer castings today with many pig irons than they did with those same brands in former years. Under the former fracture buying, the foundryman at least could select the strongest metal, as judged by the sledge, from various brands of similar fracture and pig section, and his results proved

Jan 1, 1927