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By R. A. Wattenbarger, H. J. Ramey

A systematic study has been made of the application of the real gas pseudo-pressure m(p) to short-time gas well testing. The m(p) function can be used in real gas flow problems to account for the variation of viscosity and z-factor with pressure. A mathematical model was solved numerically to generate solutions of various real gas flow problems. The effects of turbulence, formation damage and wellbore storage were included in the model. The analysis of simulated well tests showed that the interpretation methods normally used for liquid flow are generally accurate when the m(p) is used. For practical rates without turbulence, the solutions are not rate-sensifive, and the flow capacity.. kh and skin effect can be determined accurately from either a buildup or a drawdown test. However, the kh calculated from a drawdown test can be significantly low when turbulence is present. A case was simulated in which this error wa.s 36 percent. Turbulence does not affect the determination of kh from buildup tests. The proper determination of kh from p and pa buildup and drawdown plots is developed by analyzing their relationship to the m(p) method. A simple equation is given that can be used for long-range gas well performance forecasting. This expression is compared with a method pre-sended by Russell et al." Introduction The formation flow capacity and wellbore damage condition can be determined for liquid-producing tests by means of buildup and drawdown tests. These tests make use of short-time pressure transient data rather than stabilized flow tests that are often used for gas well testing. Tracy' presented a method of gas well testing that was based on ideal gas equations and utilized p2 buildup plots. This method was shown to be good for low pressure wells. MatthewsZ suggested plotting p and using an average slope and average gas properties. This method was more successful on high pressure wells. Al-Hussainy, Ramey and Crawfordh howed that variation in gas properties could be simplified by using the real gas pseu do-pressure m(p). Some cases showed that the use of the m(p) function Original manuscript received in Society of Petroleum Engineers office Aug. 8. 1967. Revised manuscript received June 11, 1968. Paper (SPE 1835) was presented at SPE 42nd Annual Fall Meeting held in Houston Tex., Oct. 1-4. 1967, and at SPE 4th Annual Eastern Regional ~eetin$ held in Pittsburgh. Pa., Nov. 2-3. 1967. 0 Copyright 1968 American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. 'References given at end of paper. provided an accurate method of interpreting buildup and drawdown tests. Because the work of Al-Hussainy et al. included only a few actual cases, there was a need to explore the use of the m(p) method for a greater variety of flow conditions. The occurrence of turbulent flow around the wellbore often is an important factor in gas well testing. Swift and Kiel,' and Carter et a1.' treated turbulence in gas well testing, but did not consider the variation of viscosity and z-factor with pressure. This paper presents the results of an investigation of the application of the m(p) method to buildup and drawdown testing. Vhe investigation included the effects of turbulence, formation damage and wellbore storage. Gas Flow Equations To formulate the mathematical model, many of the assumptions usually used in well testing theory are applied. The system has radial geometry with a closed outer boundary and is composed of a horizontal porous formation that has uniform and isotropic rock properties and uniform thickness. Allowance is made, however, for a radial region of reduced permeability near the wellbore. This region represents formation damage. The geometry of the system is shown in Fig. 1. Darcy's law does not always apply to gas flow. A more general expression is needed for non-Darcy, or "turbulent" REGION OF DAMAGED PERMEABILITY SEALED BOUNDARIES ClRCULAR WELL BORE Fig. 1—Radial flow model. AUGUST, BT7

Jan 1, 1969

By Gilbert Soler

Producers of alloy steels recognize the importance of chemical composition in relation to the hot-working properties and the typical surface defects found in their product. Each analysis of steel has its own peculiar characteristics. Under conditions of standard mill practice each analysis is susceptible to certain types of defects. Mill practice must be varied to obtain the best combination of surface and internal quality in the product. Chemical composition influences the cast structure and crystallization characteristics of the ingot. It also determines the rate of heating and cooling, the plastic hot-working range, and the phase structure of the steel at various temperatures. as well as the tendency toward scale formation and decarburization. This paper endeavors to emphasize the manner in which chemical composition affects the various properties of steel, and to indicate the relative importance of these factors in relation to the hot-working properties and surface characteristics of killed steel. The influence of chemical composition may be outlined as follows: I. Effect on the cast structure of steel, including: A. State of deoxidation, and type of inclusions. B. Gas content of steel. C. Freezing point and melting point of steel. D. Crystallization characteristics and segregation. 11. Effect on the hot-working properties and surface characteristics of steel, including: A. Plastic hot-working range. B. Phase structures at hot-working temperatures. C. Rate of heating. D. Cooling characteristics. E. Scale formation. F. Surface decarburization. EFferect of Chemical Composition on Cast Structure of Steel State of Deoxidation and Type of Inclu-sions.—The state of deoxidation is limited by the final chemical analysis desired in the finished product, and is controlled primarily by carbon, manganese, silicon, and aluminum, and to a lesser degree by chromium, titanium, vanadium, or other deoxidizing elements. The degree of deoxidation affects the density of the cast structure and broadly classifies the steel as killed, semikilled, or rimming. This in turn manifests itself in surface characteristics. The manner and extent of deoxidation also controls the amount, type, and distribution of nonmetallic inclusions formed. The equilibrium of manganese, silicon and aluminum with the slags and pouring refractories with which the metal comes in contact is important, especially in regard to inclusions of fire-clay origin. Some surface Seams and hot-working difficulties can be traced to nonmetallic inclusions.

Jan 1, 1941

By Gilbert Soler

Producers of alloy steels recognize the importance of chemical composition in relation to the hot-working properties and the typical surface defects found in their product. Each analysis of steel has its own peculiar characteristics. Under conditions of standard mill practice each analysis is susceptible to certain types of defects. Mill practice must be varied to obtain the best combination of surface and internal quality in the product. Chemical composition influences the cast structure and crystallization characteristics of the ingot. It also determines the rate of heating and cooling, the plastic hot-working range, and the phase structure of the steel at various temperatures. as well as the tendency toward scale formation and decarburization. This paper endeavors to emphasize the manner in which chemical composition affects the various properties of steel, and to indicate the relative importance of these factors in relation to the hot-working properties and surface characteristics of killed steel. The influence of chemical composition may be outlined as follows: I. Effect on the cast structure of steel, including: A. State of deoxidation, and type of inclusions. B. Gas content of steel. C. Freezing point and melting point of steel. D. Crystallization characteristics and segregation. 11. Effect on the hot-working properties and surface characteristics of steel, including: A. Plastic hot-working range. B. Phase structures at hot-working temperatures. C. Rate of heating. D. Cooling characteristics. E. Scale formation. F. Surface decarburization. EFferect of Chemical Composition on Cast Structure of Steel State of Deoxidation and Type of Inclu-sions.—The state of deoxidation is limited by the final chemical analysis desired in the finished product, and is controlled primarily by carbon, manganese, silicon, and aluminum, and to a lesser degree by chromium, titanium, vanadium, or other deoxidizing elements. The degree of deoxidation affects the density of the cast structure and broadly classifies the steel as killed, semikilled, or rimming. This in turn manifests itself in surface characteristics. The manner and extent of deoxidation also controls the amount, type, and distribution of nonmetallic inclusions formed. The equilibrium of manganese, silicon and aluminum with the slags and pouring refractories with which the metal comes in contact is important, especially in regard to inclusions of fire-clay origin. Some surface Seams and hot-working difficulties can be traced to nonmetallic inclusions.

Jan 1, 1941

By L. R. van Wert

CAREFUL research into the nature of the metallic state has yet to discover, with any certainty, its essential quality. We do riot yet know, for sure, what it is that makes the metallic elements different from, if not actually unique among, all created things. We do know, of course, that metals have certain more or less characteristic properties-they are hard, strong, and tough, and good conductors of heat and electricity, and these so-called metallic properties provide a definition of a sort. How- ever, it is the structure rather than the behavior of the metals which gives the really fundamental information necessary to the understanding of metallicity. But this information is not easily obtained. Nature has a way of keeping secrets. But happily we do possess some knowledge of how a metal is built up, and it is this matter, rather than the presentation of a formal definition, that will be discussed here.

Jan 1, 1937

Jan 1, 1969

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. TEMPERATURES AND UNDERGROUND WATERS Surface Temperatures.-The average surface dry-bulb temperature at Superior is 72.4°; wet-bulb, 57.4°; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the down-cast shafts; however, the variation between winter and summer causes a difference of only 2° to 3° in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.-Rock temperatures on the deeper levels of tile mine are as follows: LEVEL DEGREES LEVEL DEGREES 2000 109 3200 127 2250 112.5 3400 130 2550 116 3600 134 2800 120 3800 137 3000 124 4000 140 There appears to be no difference in rock temperature for any particu-lar horizon of the various formations or in the vein. Water encountered is always the same temperature as the rock from which it flows, and for this reason it is thought that the water is heated by the rock; not the rock by the water. The country rock apparently has been heated by the various intrusions, perhaps the vein itself, and has not yet had time to cool off. The geothermal gradient (Fig. 2) as indicated by the rock tem-peratures given above is 1 1/2 ° per 100 feet.

Jan 1, 1938

By Henry Fernald

THE accounting system or bookkeeping methods of any company are principally the concern of that company and of those who are in control of its affairs. Its published financial report is, however, primarily intended for those who are not already fully informed regarding its operations and finances. Whatever may be the advantages of standardization of accounting and bookkeeping methods, it must be admitted that a company has a certain right to handle its accounts and keep its books and records in whatever manner may seem to it best adapted to its affairs, even though such methods may differ materially from those generally adopted by others. In its financial reports it should not, however, either ask or expect that the statements it makes or the terms which it uses will be given in its case a meaning and interpretation different from that which they are ordinarily considered to have inn similar reports and statements of other companies. The particular form and arrangement of such reports is a matter concerning which there may be much difference of opinion. It is of little importance whether current assets come first or last in the Balance Sheet, but it is important that there should not be included under this designation any items which are not properly current assets within the generally accepted meaning of that term. The extent to which stockholders or others interested are to be made acquainted with the full details of a company's business is a question which the proper authorities must in each case decide. It should, however, be recognized that there are certain facts regarding a mining company which must be set forth in a financial statement if it is fully to cover the conditions and affairs of the company. For example, a financial statement which does not include or is not accompanied by a statement of the ore reserves of the company does not fully set forth its financial condition. This is true whether the absence of such a statement of ore reserves is because it is not desired to make public the figures or whether it is because the ore reserves themselves are not definitely known or accurately measured.

Jan 1, 1928

By J. Kent Smith

THE object of this investigation was to ascertain the effect of varying percentages of beryllium upon pure copper and the properties of the resultant alloys in their softest condition, the effect of heat hardening on them, and the extents to which these properties could be augmented by different combinations of heat hardening and cold rolling. The data compiled in this paper represent partial results of continuing work done by the writer during the years 1930 and 1931, which was a continuation of the unpublished ground work incepted in the laboratory of the Beryllium Corporation of America by H. B. Pulsifer in the year 1926. A short bibliography on beryllium alloys is appended to this paper. It has, of course, long been known that copper subjected to cold work is hardened and strengthened to a considerable extent, furthermore it had been qualitatively noted in previous experiments that copper-beryllium alloys seemed to take on hardness and strength as the result of cold work at a greater rate even than does plain copper. It was decided therefore to endeavor quantitatively to determine such rate of increase, as also the relative increases by combinations of cold working and heat hardening. The results are summarized in Tables 3, 4 and 5. A preliminary series of experiments had indicated that by an exposure to the heat of 575° F. for 2 1/2 hr. age-hardening of a 2.50 per cent beryllium-copper alloy took place. Slab ingots of nine different beryllium-copper alloys were prepared under identical conditions by means of the addition of a previously prepared 12.5 per cent beryllium-copper alloy to well melted and deoxidized pure copper. The ingots were then reduced by hot rolling to 12 gage (about 0.080 in.). These strips were heated to 1450° F. and quenched in cold water, and thus brought to their softest condition. (See Table 1.) Strips were next "precipitation-hardened" by reheating to a definite temperature. Similar strips to those itemized in Table 1 (which had been quenched from 1450° F.) were reheated for varying periods of time at 575° F. The hardness figures show that a metastable condition, of which the range of stability is dependent entirely upon time at the given temperature, begins to be noted in copper samples containing as little as 0.85 per cent beryllium. It is extremely noticeable in samples containing

Jan 1, 1932

By Barry S. Epstein

Financing the acquisition of a going coal mine operation has not had the exposure other finance-oriented projects have had. Therefore, C.I.T. feels that coal mining people and financial people should improve their understanding of the factors involved in this important type of acquisition. The discussion consists of two major subjects: analysis of the acquisition of the property, and sources and terms of funding the acquisition. Source and Terms of Funding There is a need to keep the competent medium-sized independent operator in the coal business, especially in these times of energy shortage. The creation of a resale market for coal mines encourages new investment in the coal mining business by medium-sized operators and their financial backers. Who provides debt and equity financing to acquire going coal mine operations and on what terms?

Jan 9, 1975

By Charles Austin

IN a recent paper the authors1 discussed the reactions to tempering of hypereutectoid steels quenched from 1000° C., as revealed by studies on changes in hardness, electrical resistivity, coercive force and metallo-graphic characteristics. The data, which related specifically to temper-ing temperatures of 550°, 650° and 710° C., for varying periods up to 125 hr., permitted the following important conclusions: 1. The rate of softening of the steels at the temperatures examined differed markedly although the steels were of "similar" general chemi-cal composition. 2. The temperature of maximum softening spread over a range from about 650° C. to the eutectoid inversion. 3. The divergence in behavior was ascribed, at least in part, to a profound difference in tendency to graphitization on annealing at sub-eutectoid temperatures. 4. The mode of spheroidization of the cementite, as revealed by metallographic studies, also varied considerably in the different steels. The purpose of the present investigation is to pursue further the study of the difference in behavior of the steels on tempering over a wider range of temperature. To this end the following features have received particular attention: 1. Comparison of temperatures of maximum softening of the various steels when the quenched samples were tempered for 5 hr. and for 75 hr. followed by furnace cooling and by quenching in water. 2. Determination of the effect of quenching temperature, prior to tempering, on the rate of softening. Quenching temperatures of 1000° and 850° C. were used in the investigations. 3. Examination of the microstructures obtained with the various heat-treatments employed.

Jan 1, 1938

By Edward H. Robie

NEVER before have the annual company reports in the mineral industry field exhibited the typo-graphical art so abundantly as does the current crop. Time was when most company reports made a drab appearance and dry reading, mostly confined to financial data and text that gave little information to the public or technical men. Now, the dollar statistics assume less importance. Considerable information is given on what is going on at the company's plants, new equipment being installed, new methods, properties under development, ore reserves and grades, and similar information of interest to professional men working in the field. We have one suggestion for further improvement: The names of the officers and directors of the company are always given, but only a few companies give the names of the principal operating officials. We think, in the case of a mine for example, that the name of the general manager, his assistant, the mine and mill superintendents, and any other top operating officials who have been largely responsible for the success of operations, are worthy of mention. The reports are now widely read and this recognition is due them. Conspicuous among the annual reports that we happen to have seen, in point of typographical attractiveness, are that of the Texas Co., celebrating its fiftieth anniversary with a gold-plated cover and gold printing inside; and that of Noranda Mines Ltd., with a red and black cover that would attract attention anywhere. Comment on economics, taxes, and labor give an excellent picture of what our industry is facing. Consider the following, from the report of the Union Oil Co. of California:

Jan 1, 1952

By Eckley B. Coxe

The subject of this paper will be treated as briefly as possible under the following heads : I. The latest designs of some of the machinery used at these collieries in the preparation of coal. 11. The means employed for elevating, conveying and transporting the coal and slate in and about the breaker. 111. The means employed for raising the coal from the mines to the top of the breaker. IV. The iron breaker as a structure. V. The preparation of the coal as effected in the iron breaker. A key to the plates and the letters and numbers designating different parts, will be found at the end of the paper. I. Preparing Coal. Anthracite coal as it comes from the mines is not marketable. The "run of mine" cannot, as in the case of bituminous coal, be sold. Anthracite, being very compact and practically free from volatile combustible matter, burns only at the surface, and it is, therefore, deemed important to have the lumps as nearly of a uniform size as possible, so that between them a large amount of surface will remain exposed to the action of the air without checking the draught too much, or allowing enough air to pass to cool the coal below the ignition-point, In other words, if the pieces of coal of the size of a chestnut and smaller are mixed with lumps of the size of an egg they fill the air-passages and prevent a free draught. It has long been recognized, therefore, that one of the most important points in preparation is to have a uniform sizing, and also to make as large a number of different sizes as can be produced without too

Jan 1, 1891

By W. Francis

OF THE methods that have been used for studying the chemical composition of coal, attack by reagents has not, in general, yielded much information. Most of the reagents used have been strong oxidants such as nitric acid or Schulze's solution. The use of a milder oxidizing agent, such as air at low temperatures, enables progressive changes in the character of the coal substance to be studied and thus helps toward an understanding of its constitution. British bituminous coals frequently have a banded structure. These bands (of four types) can be separated one from another and have been found to possess markedly different chemical characteristics, even when taken from contiguous portions of the same lump coal. It has been found convenient to give each of the ingredients of banded coal a distinctive name, more or less descriptive of its appearance, and the study of the chemistry of bituminous "coal" in England has resolved itself into a study of each ingredient separately. . The coal chosen for this work was taken from the Top Hard seam at East Kirkby colliery, Nottinghamshire, a detailed chemical analysis of which has been recorded by Baranov and Francis.1 The banded structure was well marked and the bands could readily be separated. The research was confined to the brilliant vitreous bands (vitrain), the dull hard bands (durain) and the "sooty partings" (fusain); for previous work had shown that the fourth type, to which the name clarain has been given, is intermediate in character, chemically, between vitrain and durain.

Jan 3, 1925

By J. E. Johnson

Charcoal-iron is quantitively so unimportant compared with coke-iron, that its qualitative importance for many industrial purposes is entirely unkriown to many coke-furnace-men, and to the great majority of the inembers of this Institute. To explain this qualitative importance, and explain some of the fact,ors that affect the quality, are the objects of this paper. A brief review of' the commercial conditions governing the charcoal-iron industry is a necessary preliminary to any adequate treatment of the subject. The advent of coke-iron, which transformed the whole iron industry commercially, left intact a limited production of charcoal-iron in the East and South, which has been conducted almays on the basis of high cost and high quality, with correspondingly high selling-price. In the Northwest, particularly in the Lake Superior district, the development has been along totally different lines, for which the close proximity of the great iron-ore deposits and the great forests of that region mere responsible. When the great white-pine forests were removed there were left behind large areas of hardwood and hemlock, to which little attention was paid in the prosperous years of the white-pine industry. But when the latter declined, the demand for lumber, and the presence of lumber-men, probably more skilled than any others in the world, caused the gradual introduction of these woods into commercial use. It was a matter of ancient knowledge that hardwood made an excellent charcoal, and to utilize the cordwood left after the saw-logs were removed, by converting it into charcoal and using it to smelt ore from the adjacent mines, mas an obvious step. In some cases the establishment of the furnace occurred in-

Jan 1, 1913

By Charles H. White

METHODS in colorimetry are based on the assumption that the intensity of the color of a definite volume of solution is directly proportional to the quantity of the color-producing substance' present. In the preparation and examination of colored solutions there are three ways in which the depth of color may be varied. These variables are; (1) the quantity of the coloring matter, (2) the quantity of the solvent, or the dilution, and (3) the thickness or depth of that portion of the solution examined. With these three variables as a basis, three general methods in colorimetry have been devised, all of which have been used in the determination of carbon in steel. In the first method, the quantity of the solution is kept the same for both the unknown steel and the standard, and the sections compared are of equal thickness, while the quantity of the standard is varied until the color obtained is of the same intensity as that produced by a definite quantity of the unknown steel. In laboratories where this method is used there is pre¬pared and kept for permanent use a series of solutions with varying amounts of the standard, representing the percentages of carbon from the lowest to the highest demanded in that laboratory. These standard solutions are kept in bottles, or test-tubes of equal diameter, and are arranged in series from the faintest to the most intense color, so that it is a simple matter to find the place of the unknown steel in the series, when the solution is of a definite volume and is contained in a tube of the same diameter as the standard tubes. In the second method, equal quantities of the standard and of the unknown steel are dissolved, the standard is diluted to a definite volume, and the solution of the unknown steel is di-

Sep 1, 1906

By Zay Jeffries

IT has been known for a number of years that certain aluminum alloys could be hardened by quenching from a temperature of about 500° C. Immediately after quenching the total increase in hardness is not marked, but the hardness increases gradually so that after about 4 days, it has reached a maximum. The actual increase in hardness probably continues for weeks or even months, but in order to detect the differences after 4 days, it is necessary to make tests at rather long intervals. So far as is known to the authors, Alfred Wilm was the first to discover these properties in aluminum alloys.1 The aluminum-copper alloys are amenable to this treatment and the addition of magnesium makes the heat-treatment effect more pronounced. Until recently heat treatment of aluminum alloys has been confined to the worked alloys in the form of sheet or extruded products. The alloy that has been most used in this connection is known commercially as duralumin and has about the following composition: copper not exceeding, 6 per cent.; magnesium not exceeding, 2 per cent.; manganese not exceeding, 1 per cent.; commercial aluminum,2 balance. A typically good alloy in this range consists of: copper, 4 per cent.; magnesium, 0.5 per cent.; manganese, 1 per cent.; commercial aluminum, balance. This alloy can be rolled into sheets or extruded; and in this condition it can be heated in the ordinary furnace atmosphere to a temperature near 500° C. and quenched in water. After about 4 days it will have the following physical properties: tensile strength 55,000 to 60,000 lb. per sq. in. (3866 to 4218 kg. per sq. cm.); elongation in 2 in., 15 to 20 per cent. No harmful effects of the furnace gases or even the air, if the heating is affected in an electric furnace in an air atmosphere,

Jan 9, 1919

By H. M. Day

THE constitution of the system silver-mercury has attracted the attention of many investigators during the last two decades, but since their results are for the most part in poor agreement, there is little need for a review of their individual contributions. It remained for the very careful thermal and microscopic investigation of Murphy1 in 1931 to give the constitutional diagram in its present and unquestioned form, which is shown in Fig. 1. He devised methods for taking cooling curves on alloys under high pressures and for the microscopic observation of alloys which contained liquid mercury as a structural constituent at ordinary temperatures. The compositions of the intermediate phases were con-firmed and supplemented through X-ray analyses by Preston and Stenbeck.3 According to Murphy, at 276° C. silver is able to dissolve 44 to 45 weight per cent of mercury, which may increase at lower tempera-tures to about 50 per cent. Preston concluded that the saturation boundary occurred at 46 ± 2 per cent at 100° C. From the values reported in the literature, these are the only ones that may be accepted as lying even in the right region.

Jan 1, 1938

By C. Scala, F. Bernstein

General expressions are derived relating the streaming potential to the electrochemical potential of a permeable junction separating two electrolytic solutions. By the methods of irreversible thermodynamics, these potentials are related to the flux of mobile species arising from differences in pressure and chemical composition. The flux is conveniently expressed as a transference number, the equivalents of a mobile species transferred through the junction per faraday of electricity. At constant pressure, the flux equation gives the electrochemical potential across the permeable junction. The streaming potential across the junction is obtained by imposing the condition of constant chemical composition. The familiar expression for the borehole SP is shown to be a particular solution of the general flux equation. The derived exprersions were verified in experiments with seven shale samples. Both the theory and experimental data provide additional proof of the presence and magniturle of the streaming potential in shales. INTRODUCTION In the interpretation of electric logs, there has been much concern over the correction to be made to the recorded SP for an electrokinetic or streaming potential originating from the difference in pressure between the mud column and the formation. It was long recognized by M. R. J. Wyllie that such an electrokinetic potential source mas in the mud cake opposite permeable sands.' More recently, M. Gondouin and C. Scala2 showed an additional but opposing electrokinetic source of potential to be in shale beds. Their work was supported by the very extensive and excellent work of Hill and Anderson.3 n the present contribution, the general relationships between the electrochemical potential and the corresponding streaming or electrokinetic potential are examined and clarified. A notable advance towards understanding the relation between the various sources of electrical potential in a borehole has been the application of the now common methods of irreversible thermodynamics to describe the passage of ions and water through charged electrolyte junctions such as in shales.' The advantages of these methods are twofold. Unlike classical thermodynamics, they can be applied to non-equilibrium sys- tems, i.e., systems in which flow takes place, provided the flow processes have reached a steady state. They also permit conventional thermodynamic properties to be related to the steady-state dynamic properties. These methods arc used here specifically to derive expressions relating the potential behavior of shales in terms of ion and water transport. Experimental verification of the expression for the shale streaming potential is given which in turn offers theoretical support to the existence of a streaming potential in shales.' Importantly, the relative contribution of transport parameters to the SP is clarified. The theoretical treatment is essentially that of Lori-mer, Boterenbrood and Hermans3 ut has been extended to derive the general expression for the SP.

By L. S. Darken

IT has been known for sometime that in an ionic lattice, such as that of Ag2S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulfide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulfide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall1 support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffusion proposed by several authors, most recently by Birchenall and Mehl.2 This theory has, however, also been questioned3.4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however, Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz,5 who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a similar mechanism, whatever it may be, at a greater or lesser rate, thus giving rise

Jan 1, 1948

By L. Seigle, R. Resnick

An inert-marker movement experiment indicates that the ratio of the intrinsic diffusion coefficients DC:DTa = 80:l in TaC at 2500°C. Measurements of the diffmion coefficient of carbon in nonstoichiometric TaC at temperatures from 1700° to 2700°C reveal that Dc increases with decreasing carbon content, but much less than expected from the probable change in vacancy concentration with carbon content. A diffusion process involving two simultaneously operating mechanisms is postulated, and shown to be theoretically feasible. The average value of the carbon diffusion coefficient is given by DC = 0.18 exp[(-85,000 ± 3000)/RT] sq cm per sec over the composition range 46 to 49.5 at. pct C. BECAUSE of their high melting points and hardness, the carbides of the IV, V, and VI group transition metals, along with those of uranium, have attracted considerable interest for applications at high temperatures. In these applications the reactivity of the materials is important, and, since rates of diffusion within the compounds influence reactivity, a knowledge of diffusion kinetics and mechanisms is desirable. While many investigations of the mechanical and electrical properties of these compounds have been made, only two fundamental investigations of diffusion in the carbides are known. Chubb, Getz, and Townleyl measured the diffusivity of carbon and uranium in UC, and Gel'd and Liubimov2 measured the diffusivity of carbon and niobium in NbC. This paper describes an investigation of the diffusion of carbon in tantalum monocarbide and, in particular, the influence of carbon deficiency on this process. Tantalum carbide melts at approximately 3800°C, which makes it one of the highest melting materials known. The compound exists over a rather wide range of carbon Content.3-7 At the peritectic temperature, 3240°C, the phase extends from about 36 to 50 at. pct C. Although the compound can exist with a substantial carbon deficiency, the high carbon phase boundary remains near the stoichiometric composition over the entire temperature range; i.e., no carbon excess is observed. The structure of TaC is the NaCl type wherein carbon atoms normally occupy the octahedral sites in a somewhat expanded fcc lattice of tantalum. Decrease of the lattice parameter with decreasing carbon suggests that the removal of carbon introduces octahedral vacancies into the lattice. I) EXPERIMENTAL DETAILS AND RESULTS Inert-Marker Experiments. In a compound such as TaC the interstitial element would be expected to diffuse more rapidly than the metal. This was confirmed by an inert-marker experiment, following Srnigelskas and irkeendall.8 Ideally, the markers should be placed at the interface between a slab of low-carbon TaC and graphite, and their movement during subsequent inter-diffusion measured. Unfortunately, no solid could be found which is unreactive in contact with carbon at the high temperatures employed in these experiments. In order to circumvent this problem, a specimen was designed in which the markers consisted of several small canals running just below the surface of a tantalum slab. This specimen was prepared by machining grooves on the surface of the tantalum slab and then diffusion-bonding a thin plate of tantalum to the slab over the grooves. The surface of the plate was then ground down until the distance between the canals and surface was as small as possible (about 0.01 cm). Thus, the canals would lie entirely within the TaC phase after a short period of diffusion. The diffusion anneal consisted of immersing the metal sample in high-purity graphite powder and heating for approximately 10 hr at 2500°C under vacuum. At this temperature, the vapor pressure is sufficiently high and the transfer of carbon from graphite sufficiently rapid to allow the surface of the diffusion sample to attain the stoichiometric carbon concentration very quickly. Conclusions regarding the relative diffusion rates of carbon and tantalum in the compound layers (TaC and Ta2C) can be drawn from the location of the canals after the diffusion anneals. If the growth of the layers is governed mainly by the diffusion of carbon, as expected, the canals should remain close to the sample surface. If the diffusion of tantalum contributes appreciably to formation of the compound layers, the distance from the markers (canals) to the surface should increase. Fig. 1 shows, diagrammatically, the appearance of the specimens after diffusion, and Table I presents the depth below the surface at which the

Jan 1, 1967