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Prospecting methods used in Tennessee have gradually improved with the years, as required by depletion of the easily accessible and shallow deposits and the universal trend toward mechanization, and as necessitated by exploring deeper beds, often occurring under limestone and flinty overburden. In the early days it was a very simple matter to dig pits by hand, using a plentiful supply of local farm labor to expose relatively shallow deposits of "brown rock" under shallow clayey overburden that would stand up without timbering. Visual inspection of the exposed phosphate and expert judgment of the "grade" analysis, aided by a "biting" test to reveal presence of unwanted silica, furnished most of the information required. All this might be helped by a few samples sent to the local chemist† who supplemented his income by judicious trading or tanning a few bear skins. The extra curricula activities did not affect the accuracy of the analysis which hold up even under present day standards. Some shot and core drilling was done in Hickman County, mostly for the limestone-like blue Phosphate deposits. The next step was the use of a 4-in. posthole auger, hand operated as described by Guenther, followed by a completely mechanized rig, as described by Pickard. Both these methods are practically adapted to the prospecting of the relatively soft brown rock deposits at moderate depths of clay overburden. For prospecting in areas of deeper overburden, such as are often found in Hickman County, up to 150 or even 200-ft depths, a modified core-drilling method is described by Guenther. Johnston describes a special diamond-drilling technique, developed by TVA, to penetrate flint horizons, which was adopted by the International Minerals in chemical corporation to prospect in Hickman County where deposits had previously been prospected at considerable expense and with difficulty, by small, temporary, hand-dug shafts.

Jan 1, 1948

By E. D. Gardner

Apparently the widespread agitation for the codification of our mining laws has had its effect, and it is quite possible that Congress will take up the question during this present session. The greatest objection to our present statutes pertaining to metalliferous deposits seems to be directed against the law of the apex. Those who are not in favor of changing this law are very far in the minority and they apparently realize that it is useless to urge its retention. Next in importance to the repeal of the law of the apex, seems to be a widespread advocacy for the repeal of the law requiring discovery of mineral before a valid location of a mining claim can be made. To a lesser extent there appears to be a desire to have the law changed so as to allow patent for claims without mineral discoveries. The purpose of this article is to review the arguments in favor of the proposed change of the discovery requirement, to show some of the evils that may be expected to result therefrom, and to consider whether a system may be devised to correct the undesirable features of the present law in this respect and at the same time not expose the mining fraternity and the general public to the evils which would result from the repeal of this fundamental requirement. Under the law as at present framed, the validity of a mining location is dependent upon the fact of discovery of mineral within the boundaries of the land claimed. " * * * but no location of a mining claim shall be made until the discovery of the vein or lode within the limits of the claim located" (Sec. 2,320, U. S. Rev. Stat.). All authorities agree that discovery is the source of the miners' title. Lindley, in his valuable work on Mines (3d Ed., Sec. 335), lays down the rule in part as follows: "Discovery is the initial fact. Without that no right can be acquired. * * * Such discovery must precede the location, or be in advance of intervening rights. The proof of recording and marking a claim will not authorize the court to presume a discovery." As is well stated by the U. S. Supreme Court in Erhard v. Boaro (113 U.S. 536):

Jan 1, 1917

By H. M. Rutherford

The reflection method in seismic prospecting has aroused much interest in the past few years. The purpose of the present paper is to present the method of reflections in the mapping of geologic structure and also to give some indication of its limitations. The reflection method is well adapted to the mapping of geologic structure in the Mid-Continent fields, and has been found most useful there. The refraction method is ideally suited to the finding of structures, such as domes, where the amount of relief is very large. This explains the brilliant success of the refraction method in the Gulf Coastal region of Texas and Louisiana. The additional fact that salt has a much higher velocity than the surrounding sediments made their discovery much easier. By the use of the reflection method, differences of relief of 25 to 50 ft. to the mile may be detected at a depth of 5000 ft., and the depth points accurately plotted on a map. This is hardly possible by the use of the refraction method. The reflection method has been in almost continuous use in the Mid-Continent area since 1926, but very little, if anything, has been published until recently'(7) † regarding either the method or the results. The discovery of several oil fields is now attributed to the use of the reflection method. Reflection methods have been used by the Germans to find the thickness of the ice of several glaciers. (2,8) The depths there considered were of the order of only a few hundred feet. For the method to be of any practical value in this country, it must be able to work to depths of several thousand feet. As was indicated above, this is now possible, though there are many problems connected with the reflection method yet to be solved. The refraction method requires that the shooting be done over long ranges. It was necessary, for example, to take distances out to several miles in order to penetrate some five thousand feet. Naturally this uses a good deal of dynamite. In the reflection method the distances are much shorter and the amounts of dynamite are much smaller, within limits which will be noted below. The chief distinction between refraction and reflection methods is to be found in the analysis of the seismo-gram. Refraction shooting makes use of only the first arrival of energy

Jan 1, 1934

By A. D. Zunkel, A. H. Larson

Equilibrium antimony contents of pb-sb alloys in contact with PbO-Sb2O3 slags containing less than 45 mole pct Sb203 uleve determined at 650', 700°, and 750°C in an inert atmosphere. In this ten~pevature range, the antimony contmzt of the alloy increased with increasing temperature at all slag compositions. The PbO-Sb203 phase diagram below 28 mole pct Sb2O3 was determined by thermal analysis and by application of a log sbZ4/y$b0 us plot determined from the equilibrium-activity data. The resulting phase diagram showed a eutectic at a temperature of 604°C and a comfiosition of 21.6 mole pct Sb2O, with a maximum terminal solid solubility of Sb203 in PbO of 5.6 mole pct. These results are compared with existing data in the literature. In the past three decades, only a small amount of experimental work has been done on the slag-metal equilibria in the Pb-PbO-SbaO3 or the analogous arsenic and tin systems. These systems are important in commercial lead-refining processes such as softening and dross fuming since it is impurities such as antimony, arsenic, and tin in lead bullion and Sb2O3, As2O3, and SnOz in lead drosses which must be re-

Jan 1, 1968

By John F. Kendrick, Paul D. Cornelius

This paper is a progress report of a study the authors are making of the sucker-rod pump, considered as a vibrating system with one degree of freedom, with forced vibrations and with viscous damping. Dr. S. Timoshenko's formula is given, defining such a system. Each factor is considered in respect to the problem of operating sucker rods, and the zone is pointed out in which the mathematics do not apply to the sucker-rod pump, because of its variable mass. This general theory is interpreted in the light of nearly two years of testing wells in the field, and correlating the results of other tests. The motion of the pumping mechanism is a vibration. The string of sucker rods vibrates with a natural frequency. The motion of the plunger is the result of adding together these two vibrations, and is modified by a damping or friction factor. The controlling factor appears to be the ratio of the period of the natural vibration of the rod string to the period of the vibration of the pump. The first conclusion is that a definite value of this ratio, which is below resonance and is probably not greater than 0.5, should not be exceeded in order to assure satisfactory performance from the sucker rods. The second conclusion is that the component parts of the pumping equipment should be selected to give the smallest practical period of the natural vibration, and when this does not permit operation at a safe speed and give the required plunger displacement, a longer polished-rod stroke should be used. While the quantitative results are but rough approximations, the qualitative analysis of pumping problems on this basis promises to be of considerable value in diagnosing the cause of poor performance and prescribing suitable remedies. The trouble that results, whenever it becomes necessary to crowd the sucker-rod pump, to take potentials or to handle increasing volumes of water, is responsible for the belief that this type of pump is not equal to present day needs, and that it is only a question of time before some other pumping device will take its place. Of the troubles experienced, it is not surprising that the frequency of sucker-rod failures should

Jan 1, 1937

By E. J. Horwood

The varying physical character and large extent of the Broken Hill lode necessarily involve the employment of a variety of underground methods. The lode had its origin in an extensive fault plane traversing metamorphosed schists conformably, as a rule, with their beds of stratification. The underground waters carrying minerals in solution deposited their contents. in the original cavities formed by the faulting action, and in the enlargements of these cavities due to dynamic forces brought to bear on the rocks, more especially on the hanging-wall side of the fault, This deposition was supplemented by metasomatic replacement of a portion of the original rock contents by the argentiferous sulphides of lead and zinc which form the staple products of the district. Although the orebody is practically continuous throughout the mines, its width varies greatly, ranging from a few feet to about 350 ft. The widest portions occur in conjunction with huge folds in the inclosing country rock, almost exclusively on the hanging-wall side. The ore it these folds pitches to the south in the southern half of the field, and to the north in the northern half; there are, however, undulations in these ore channels evidently due to compression of the rocks in the direction of the channels. In the earlier days, before the orebodies had been opened up: vertical cross-sections across these bulges in the hanging wall gave the lode the appearance of the "saddle formation," so well exemplified at Bendigo in Victoria; but subsequent development of the ore channels ha; long since proved that the formations in the two districts are entirely different. The depth reached by the zone of complete oxidation of the sulphide, varies from about 250 to 550 ft. from the original outcrop while partial oxidation extends in places below the 1,000-ft. level. The result of oxidizing influences has been the production of ore of every grade of cohesiveness, from that of dry sand to that of hard compact rock.

Jan 1, 1916

By H. I. Altshuler

THE mines operated by the Compañia de Real del Monte y Pachuca, Pachuca, Mexico, are in two districts, the Pachuca, and Real del Monte. The principal area of mineralization is within a rectangle roughly 10 miles from east to west and 6 miles from north to south. It contains a number of veins from 2 to 20 ft. wide, which are exploited by this mining company. The scattered position of the producing mines led to the construction of two mills between 1906 and 1908; the Loreto mill, in Pachuca, averaged 2600 tons daily, and the Guerrero mill, in Real del Monte, milled 1270 tons daily. On Feb. 1, 1929, the management decided to enlarge the Loreto mill to take the combined tonnage of both mills at that time. This economic measure required the centralization of ore delivery, which would also afford a material saving in the cost of ore transport. The centralization would give the company the following advantages over the former system of operation: 1. Beneficiation at a single mill, closer to source of materials and supplies than the abandoned- Guerrero mill. The refinery is, also in the Loreto patio. 2. Ore delivery to surface at one point (San Juan Pachuca shaft) instead of at four. 3. Elimination of aerial tramways. To show what would be required to effect this centralization, it is necessary to describe the means by which the ore was delivered to the two mills, prior to centralization. The heart of the Real del Monte district is roughly four miles from that of the Pachuca section. The producing mines in these two districts were: Pachuca district: Santa Ana mine Camelia group

Jan 1, 1934

By T. V. Moore, H. D. Wilde

In many of the important problems of the petroleum engineer, it is necessary to know accurately the laws governing the flow of gas and liquid mixtures in vertical pipes. Although much work has been done along these lines, no satisfactory solution to the problem has been found. A good theoretical discussion of the energy balance in a gas-lift has been published by Versluys.1 One of the most important factors affecting the efficiency of the flow of oil and gas mixtures is slippage, and in most of the experimental work that has been done no provision has been made for the measurement of this quantity. As Versluys pointed out, since there is no method now known to estimate it from the data usually taken, slippage must be determined empirically. This paper presents the results of some work carried on to measure slippage in short experimental gas-lifts. As shown herein, slippage can be easily calculated in a vertical pipe carrying a mixture of oil and gas if the fractions of the pipe occupied by liquid and gas respectively are known. In this work, the fraction of the pipe occupied by the liquid was measured under a wide variety of conditions and the relationship between this fraction and other quantities, which are easily measured in ordinary work, was determined. It was hoped that the quantitative relationship obtained from this work could be used for making accurate calculations in flowing or gas-lift wells, but unfortunately it did not check satisfactorily when applied to actual wells. Apparently flow in long flow pipes is more efficient than in the short ones used for the experimental work. Nevertheless, it is felt that the data themselves arc of interest; that the method of attack may be of value in future work and that the relationship derived between slip and the relative velocities is a contribution toward the solution of the gas-lift problem.

Jan 1, 1931

By Robert S. Archer, Zay Jeffries

It is about fifteen years since the development in Germany, largely by Alfred Wilm, of the aluminum alloy called duralumin. In this alloy, combining as it does the tensile strength of mild steel with the lightness and corrosion resistance of aluminum, a distinctly new material was presented to the engineering world. Despite the evident usefulness of this material, however, its commercial development has been slow, due in part to the difficulties involved in its fabrication. In view of the potentially great utility of strong aluminum alloys, it seemed desirable to find means of producing such alloys with better fabricating properties, and work was undertaken with this object in the laboratories of the Aluminum Company of America several years ago. This work has resulted in the production of two new types of aluminum alloy of the "strong alloy" class, having distinctly improved fabricating qualities. The knowledge gained has also made it possible to produce alloys of the duralumin type with greater strength and hardness than previously obtained. There have thus been made available some new engineering materials which it is the object of this paper to describe. These alloys, induding duralumin, are fundamentally wrought alloys. Castings of the same compositions heat treated in the same manner give inferior physical properties, particularly as to ductility. The statements made subsequently concerning properties and heat treatment apply to material that has received sufficient working to thoroughly break down the cast structure. The material referred to has, in general, undergone a reduction in section of at least 80 per cent, by mechanical working. It may be mentioned in passing that other compositions have been found that are suitable for the production of the maximum physical properties in heat-treated castings.

Jan 1, 1925

AS IS evident from the discussion in previous chapters, the methods by which an open-hearth heat may be made are numerous, but any heat, in the ingot form, may be classified as one of three types, depending upon the degree of deoxidation to which the metal is subjected. These are rimmed, semikilled, and killed, and desirable ingot structures, from the standpoint of distribution of porosity, are illustrated in Fig. 63. These are the most useful types of ingot structure [ ] and represent three stages in the continuous series from "wild" to "dead killed" (see Fig. 23, page 46) ; some of the variations of each type are discussed later in the chapter. The choice of ingot structure and of finishing practice used to produce the desired metal action in the molds is determined by consideration of: 1. Specified final analysis. As an example, the production of rimmed steels is mostly limited to carbon contents below 0.30 per cent and manganese contents below 0.60 per cent; on the other hand the production of low-carbon killed steel requires greater care.

Jan 1, 1944

By Norman Hedley, George Barsky, S. J. Sawinson

The cyanidation of precious-metal ores is a complex chemical process. Numerous reactions occur, some of which cause an undesired consumption of alkali and of cyanide. A knowledge of these reactions, their products, and the factors that influence the rates at which they proceed should be of value in working out the most economical conditions for cyanidation; but at present, much of this knowledge is lacking. This paper is confined to a study of some of the fundamentals of cyanidation. At the start of such an investigation it is necessary to simplify the problem under consideration by eliminating as many variables as possible. The results are then, of course, not immediately applicable to practice, but it is hoped in further work to round out the information and thereby make it of more practical value. For convenience in presentation, the paper has been divided into two parts, one devoted to a study of the reaction between cyanide and gold or silver, the other to a consideration of the factors that determine the rate of dissolution. I. REACTIONS INVOLVED IN DISSOLUTION OF GOLD AND SILVER IN DILUTE CYANIDE SOLUTIONS Ever since the cyanide process for gold and silver extraction was introduced there has been discussion of the equation representing the reactions involved. In undertaking a detailed study of these factors, it was felt that the most logical first step was to determine, if possible, what reactions could theoretically take place when gold and sill-er are dissolved by dilute cyanide solutions. It is possible to determine whether or not a given reaction will theoretically take place by calculating the free energy of the reaction. This free-energy value for any given reaction is the algebraic sum of the free energies of formation of each of the reactants and products, and, if these values are known, the calculation is simple. (A chemical change always involves an energy change and the amount of energy change involved is the factor determining whether a given reaction will take place or how far it will go. In chemistry we consider what is known as the "free energy"; that is, the maximum amount of energy that can be utilized as

Jan 1, 1935

By C. P. Proctor, J. T. Crawford

TROUGH washers were among the earliest methods used for concentrating ores; they are referred to by Agricola about the middle of the sixteenth century as already being used while the hand- operated jigging sieve had only recently come into use. For cleaning coal the trough washer apparently was first used in France and Belgium about 1841. The early trough washers were intermittent and the refuse at least was shoveled out by hand. The invention of a continuous jig washer, by a Frenchman, Berard, in 1848, acted as a stimulus to coal washings in jigs and retarded progress in trough washing in the nineteenth century. Chapman and Mott' describe a number of trough washers developed in England and on the Continent from 1850 to 1900, such as the Bell and Ramsay, Ramsay, Bell and Green, Wunderlich, Scaife, McLellan, Lodge, Elliott, Blackett, and Murton. The later of these removed the refuse mechanically, either intermittently or continuously, but in ways that interfered with stratification.

Jan 1, 1943

By Anton Eilers, R. W. Raymond, O. H. Hann

THIS paper will treat of such works only as beneficiate ores directly in the mining districts. And when it is said that more than twenty

By T. S. Fuller

Various phases of the embrittlement of solid copper containing oxygen by the action of reducing gases at high temperatures are familiar to readers of metallurgical literature through the work of many experimenters. In 1900, Heynl recorded observations of copper being heated in hydrogen with the development of fine cracks, the result of the formation of steam within the metal through the action of hydrogen on the copper oxide usually found in copper. Archbutt,2 in 1905, published the results of experiments, showing that all oxygen can be removed from copper by heating to redness, for several hours, in hydrogen. Intercrystalline cracks and extreme brittle-ness developed. Archbutt attributed the brittleness to the reduction of oxides present in the copper. Bengough and Hil1,3 in 1910, encountered the now well-known embrittlement at the outset of their investigation and stated in their paper: It soon became evident that the effect of any heat treatment depended largely on the presence or absence of reducing gases in the atmosphere of the furnace, as well as on its temperature. Hence it became necessary to adopt a somewhat elaborate scheme of heat treatment. The authors found embrittlement in separate experiments due to both hydrogen and carbon monoxide and concluded that: "The gases ruin the alloys after being heated to about 650" C. in their presence." Ruder,4 in 1916, reported the results of a series of experiments made by heating commercial and deoxidized copper in hydrogen, carbon monoxide, carbon dioxide, and steam. In agreement with other writers, he found that copper containing oxygen was made brittle by reducing gases, while the deoxidized metal remained unaffected. In the case of

Jan 1, 1926

By Gordon G. Bentle, W. P. Fishel

GREINER, Marsh, and Stoughton1 have reviewed the literature in a monograph on the iron-silicon system. The lack of agreement among the various studies may be due to the difference in the purity of materials in some cases. The results of the X-ray method indicate only a general rather than a specific limit of the y loop. The iron-titanium system was investigated by Roe and Fishel,' whose results are used in determining the iron-silicon-titanium y loop. The literature indicates that no study has been made thus far of the iron-silicon-titanium system in the y loop region. Experimental Procedure The alloys were made from Armco iron, 99.86 pct Si, and 98.5 pct Ti. The titanium contains 1.07 pct Fe. The Armco iron contains 0.01 pct C, 0.005 pct Si, 0.02 pct Mn, 0.006 pct P, 0.01 pct S, and 0.04 pct Cu. A dilatation sample of Armco iron was prepared in the same manner as were the other samples. Several dilatation runs indicated that Ac3 begins at 905°C and ends at 910°C, which compares favorably with the study of Wells, Ackley, and Mehl' employing specially purified iron. All alloys were melted in an induction furnace in Alundum crucibles and were top poured into baked core sand molds. The ingots weighed about 600 g as cast. Dilatation samples of 4 in. by % in. diam were taken from the bottom end of the ingot, from which turnings for analysis were taken. Turnings from each end of two of the samples indicated that the alloys possessed uniform silicon content. A hole was drilled halfway through each end of a 4 in, dilatation sample. A chromel-alumel thermocouple was inserted in each hole and the surrounding metal peened in to hold the thermocouple in place. Fig. 1 represents the dilatation apparatus. The heating unit is an Alundum tube wound with resistance wire; the dilatation tube is a McDanel combustion tube; the push rod is zircon; the dial gage is graduated in 0.0001 in. and was vibrated to prevent sticking. A blank run over the temperature range of interest gave no significant dilatation. The thermocouples were attached to a multiple recording micromax which indicated the temperature at each end of the sample at 35 sec intervals. A Lindberg control unit governed the rate of heating of the furnace, and lowering or raising the

Jan 1, 1957

By E. L. Dougherty, J. W. Sheldon

A numerical method for computing the dynamical behavior of fluid- fluid interfaces is described. Results of studies made to assess the accuracy and economy of the method on a computer are reported. It is concluded that it is practical to obtain digital computer solutions for fluid- fluid interface problems with two space dimensions. PROBLEM DEFINITION We consider two-dimensional flow in a rectangle as shown in Fig. 1, where a fluid-fluid interface divides the rectangle into two regions. The pressure is specified along the lower boundary (the injection boundary) and upper boundary (the withdrawal boundary). There is to be no flow of fluid across the side boundaries, which are walls of symmetry for the flow, and px = 0 along these boundaries. The fluids are incompressible, the absolute permeability and porosity is constant, and each fluid has its own constant mobility. Thus, the pressure satisfies Laplace's equation in each region. Across the interface, pressure is continuous and the normal component of fluid flux is 1. These conditions are shown in Fig. 1. The velocity of a point on the interface in the direction of the normal from Fluid 1 into Fluid 2 is U,/ Q, where Un is the normal component of volumetric flux at the point on the interface, i.e., For brevity, we call the problem defined above "Problem A". Problem A is a simple example of a dynamical fluid-fluid interface problem. However, the same numerical methods which we use to solve Problem A can be extended to the solution of a large number of fluid-fluid interface problems which are mathematical models for various oil recovery processes,l hence our interest in Problem A. We define the interface by prescribing the x, y coordinates of a finite set of points. These points are called "interface mesh points" and are illustrated by triangles or asterisks in the figures. Fig. 2 is a procedural (flow) chart displaying the main steps in the solution. We comment briefly on some of these steps in this section and then give further details in subsequent sections. For mobility ratio greater than one it is well known that Problem A is unstable.*2 Small amplitude,

Jan 1, 1965

By David White

IN these days, when detailed investigations of stratigraphy, structure, and sand conditions so frequently result in the discovery of new oil fields, and applause from oil companies and the public, geologists do well to walk humbly, and punctiliously to admit that the geologic principles controlling the distribution of oil and gas have as yet been discovered only in part, and that what remains yet to be learned is probably vastly more than what is already known. The few experiments already at-tempted have been fragmentary, and somewhat desultory, and however positive each of us may be with respect to certain theoretical conclusions, many of the fundamental questions as to the origin and mode of occurrence of petroleum are subject to radical disagreement. Of the chemical changes attending the generation of petroleum from organic matter, little is actually known. Most of the postulated formulas are liable to be misleading, through ignorance of essential factors. Open-mindedness is therefore a prime essential at the present stage of our science. Nevertheless, adopting the hypothesis that oil originates in some manner fundamentally connected with the organic theory, and in possible departure from such open-mindedness, the writer will pay no attention to the so-called inorganic theory, since every attempt to apply this theory to the study of old oil fields, or to the discovery of new ones, affords cumulative evidence of its inadequacy. In this paper, some of the factors affecting the occurrence of petroleum that the writer believes worthy of consideration by the prospector for oil in any new region will be discussed. Some of these, which are less generally understood, will be considered somewhat in detail. Other points, the significance of which cannot now be determined, require more field study, and for that reason are here brought to the attention of the field geologist. On the other hand, certain theoretical points which do not bear especially on the oil possibilities of a new region will be given little

Jan 2, 1920

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

By F. M. Perkins, R. H. Jamison

Publications concerning scaling laws for laboratory flow models of oil reservoirs indicate that the relative permeability and capillary pressure relations must be the same functions of saturation in the model and its prototype. In this paper, the relative permeabilities and saturations are redefined in a way which permits one to have diflerent relative permeability and capillary pressure relations in the model and prototype. The development of the new scaling criteria is demonstrated by deriving scaling laws for one simple flow problem. INTRODUCTION The successful application of information gathered through bench-scale model studies to the prediction of multi-phase fluid flow behavior in petroleum reservoirs requires careful consideration of the scaling criteria. The requirements which must be met for a small-scale model to duplicate the behavior of a much larger reservoir prototype have been discussed by Leverett, et al,' Rapoport,2 and Geertsma, et al.3 According to these authors, the relative permeabilities to water, oil and gas and the dimensionless capillary pressures must be the must have the same values in the model and prototype. Furthermore, they point out that the viscosity ratios must have the same values in the model and prototype. In addition to these requirements, other scaling criteria are given which, when considered, usually dictate a much higher permeability in the model than exists in the reservoir. Since the more permeable model sands may have connate-water and residual oil saturations quite different from those in the prototype, the scaling requirements pertaining to the dependence of relative permeabilities and dimension l ess capillary pressures on saturation usually are not met. Also, if the model fluids are selected to give equal viscosity ratios in the model and prototype, one may find greatly different mobility ratios* in the two cases and, therefore, may expect grossly different flow patterns. For this reason, Craig, et al,' correlated the results of their model studies with mo- bility ratio rather than with viscosity ratio. As yet, however, no satisfactory method has been advanced which permits use of anything other than the scaling requirements outlined in the previously mentioned papers. The purpose of this paper is to present a method of developing a set of scaling criteria which permits different relationships between saturation and relative permeability or capillary pressure in the model and prototype. Rather than attempt to report scaling criteria for a variety of practical situations, this paper demonstrates by use of one simple example how the modified scaling criteria are derived.

By E. P. Miller, F. R. Morral

Hot-dipped heat-treated zinc coatings on sheet steel were examined with X-rays. The phases identified were compared with those listed in the modern literature 01 the zinc-iron system. The zeta (FeZn13) phase is shown to correspond to the phase found by Schueler (1925) in heat-treated zinc coatings. An investigation was undertaken to determine the phases present in hot-dipped heat-treated zinc coatings on steel sheets and wire. This kind of coating on wire was studied some years ago by Schuelerl by microscopic and chemical methods. He reported a new phase, FeZn10. Later, Clark and Stillwell,2 using X-ray crystal analysis, identified a new phase in ordinary galva. nized wire, which was assumed to be the FeZn10 phase. Since the extensive review of the iron-zinc alloys presented a few years ago,3 much new work has been published, some of which5-l6 was too late to be included in the recent edition (1939) of the American Society for Metals' Handbook.4 Figs. 1 and 2 are reproductions of the latest iron-zinc diagram proposed by Schramml1 as a result of his investigations by microscopic, thermal, magnetic susceptibility and X-ray methods. Table 1 summarizes all the known published X-ray data of the phases Present. The solubility of iron in zinc has been determined by x-ray methods.10 In the same manner the homogeneity range of the P phase was studiedlo using the principle that the parameter of an intermetallic compound changes while the concentration of One of the constituents changes. Schramm10 has found some 80 alpha lines in X-ray powder photograms of phase d1, and from these he believes that this phase is related to the P phase. Previous investi-

Jan 1, 1941