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By C. G. Dunn, F. W. Daniels, M. J. Bolton

Recent observations on grain boundary movements in sihcon iron have indicated the possibility of studying grain growth phenomena in two-grain specimens in which several variables affecting growth are readily controlled. These variables are (1) the energy per unit area (?) in the grain boundary, (2) the orientation relationship of the two grains, and (3) the radius of curvature (7) of the moving boundary. Ideally, one grain A should be a narrow rectangular parallelepiped adjacent to a second grain ß as shown two dimensionally in Fig 1. Such a two-grain group becomes unstable when one end of grain A is shaped according to the dotted line. Since the width w of grain A remains constant during growth of grain B, T should also remain constant. The other vari- ables mentioned above can be controlled in the preparation of each two-grain specimen.l,2,3 For a parLicular orientation of each grain, is not necessarily fixed; ? may also depend on the orientation of the grain boundary, but this may be controlled to some degree. The energy relationships for the gowth of grain ß may be derived from the more simple arrangement of two grains A' and B' shown schematically in Fig 2. Here B' largely surrounds A'. Assume these grains are oriented with a common plane parallel with the flat

Jan 1, 1950

LIST OF MEMBERS, ASSOCIATES AND JUNIOR ASSOCIATES ALPHABETICALLY ARRANGED ||Abad, Leopoldo F, College of Min, Univ of California Berkeley, Cal '23 ||Abarquez, Ramon F, Met, Bureau of Seience Manila, P I '24 ||Abbey, Robert Graham, Student, Case School of Applied Science Cleveland, Ohio '21 Abbort, A N , Mines Supt , Mazapil Copper Co , Ltd Concepcion del Oro, Zacatecas, Mexieo '23 Abbott, Clarence E , Gen'l Supt , Iron Mines Div , Tenn Coal, Iron & R R Co , 1405 Minnesota Ave , Bessemer, Ala '04 Abbott, Louis Benjamin, Chief Engr, Consolidation Coal Co, Elkhorn Div Jenkins, Ky '15 Abbott, Robert R , Met Engr , Peerless Motor Car Co Cleveland, Ohio '12 ||Abbott, Wells Osborn, Ray Consolidated Copper Co Hayden, Ariz '23 Abeel, George H, Jr, Cons Min Engr 4812 W 17th St, Los Angeles, Cal '18 Abel, Albert E, Asst to Pres, Valley Mould & Iron Corpn Sharpsville, Pa '19 Abeloff, Miran S Address Wanted '21 Abernathy, G E, Kansas State Teachers College Pittsburg, Kans '20 Abey, Hiroshi, Min & Met Engr. Takata & Co, 2 Yeirakucho, Niehome, Kolimachi-ku, Tokyo, Japan '17 ||Aborn, Robert H 24 Groveland St, Auburndale, Mass '19 Abouchar, Sylvain Sley, Min Engr & Geol , Care of S H Sekaly, 13 Rue El Nimr, Cario, Egypt '17 Abraham, Arthur W 1828 N Alexandria Ave, Los Angeles, Cal '20 Abrahams, A. I 115 East 82nd St. New York, N Y '14 ||Abrahamson, C. Walter, Min Engr, Brule Min Co Stambaugh, Mich '21 Abrams, Charles Jackson Columbia Bldg, Spokane, Wash '21 Abrams, David H, Min Engr, S E Dickey & Co, 809-11 Johnstown Trust Bldg, Johnstown, Pa '20 Acker, E 01C, Met 128 East Washington Lane, Germantown, Philadelphia, Pa '86 Acker, William L, Diamond Drill Contractor Mears Bldg, Scranton, Pa '18 Ackerman, Ernest R, Pres Lawrenee Portland Cement Co Plainfield, Union Co, N J '15 Adachi, Jinzoo 11 Shiba Park, Shiba-Ku, Tokyo, Japan '88 Adachi, Yuich, Meeh Engr, Anzan Steel Works, Anzan, South Manchuria, China, (Via Dairen) '21

Jan 1, 1923

By P. Bolsaitis, L. Skolnick

A model of metallic solutions is postulated which explains the energy of formation of alloys on the basis of changes in electron density around solute and solvent atoms and changes in pairwise interactions between atoms. The model is based on the Wigner-Seitz cell model of metals, with the electronegativities of the metals as the parameter for the electron-attracting power of the constituent atoms. In contrast to models based on the description of cohesive energy in terms of pairwise interactions only, which require an empirical, adjustable correction parameter to the Berthe-lot relations in order to predict negative energies of formation, the electron cell model accounts for both negative and positive energies on the basis of parameters of the pure components. Calculated heats of mixing based on published parameters of the pure metals are found to compare favorably to experimental values, despite the absence of any adjustable parameters in the model. THE formulation of an "exact" quantum mechanical model for the energy of cohesion of metals reduces ultimately to the many-body problem and for a complete solution would require the knowledge of wave functions and energy levels of all the particles in the system. The case of alloys is further complicated by the fact that the potential fields around the constituent atoms are different and the matching of boundary conditions in terms of the resulting wave functions is still an unresolved mathematical problem. It appears that in spite of the numerous investigations that have led to an elucidation of many properties of the metallic state, the formulation of the Hume-Rothery rules in 1931 marks the lone accomplishment toward simple, qualitative prediction of the energy of formation of alloys. More recently Friedel'' and Arafa have utilized the modern concepts of the electronic structure in metals in combination with the Hume-Rothery rules to arrive at quantitative estimates of the energy of formation of alloys with low solute contents. The relative success of the Hume-Rothery rules and Friedel's and Arafa's studies encouraged broaching the subject of formulation of a model based on realistic physical parameters and of conceptual and mathematical simplicity that could be applied to alloys regardless of concentration. On the basis of the free-electron theory, the cohesive energy of pure metals can be expressed as a function of "valence" (number of free electrons per atom), lattice parameter (or density), and the ioniza-tion energy. In addition to the electronic contributions to cohesion, one has to consider the pairwise exchange interaction energy between neighboring ion cores and the contribution from van der Waals forces. The energy changes upon alloying are viewed as resulting primarily from a redistribution of electron densities around the ions (a simplification of the more basic concept of a change of the wave functions of the electrons in the presence of a perturbing potential field). In addition there is a change in the pairwise interactions between neighboring ions which is usually the only factor taken into account in commonly used adaptations of the quasichemical theory. The electronegativities of the metals forming the alloy are used as the measure of the electron-attracting power of the ions in the alloy and the difference in electronegativities as the driving force for changes in electron energy on alloying. The interplay of pairwise interactions and electronic forces results in positive or negative energies of formation of alloys. Results obtained for systems to which the free electron model is best applicable are in good agreement with experimental values. 1) COHESIVE ENERGY OF METALS IN TERMS OF THE ELECTRON CELL MODEL The simplest physical model of a metal is that of a lattice of positive charges immersed in a sea of uniform, negative charge distribution represented by the

Jan 1, 1969

By N. A. Gokcen, John Chipman

SILICON is the most commonly used deoxidizer and an important alloying element in steelmak-ing; hence a detailed study of this element in liquid iron containing oxygen is of considerable interest. The equilibrium between silicon and oxygen in liquid iron has been studied by a number of investigators but generally with inconclusive or incomplete results. The variation of the activity coefficients of silicon and oxygen with composition is entirely unknown. Published investigations deal with the reaction of dissolved oxygen with silicon in liquid iron and the results are expressed in terms of a deoxidation product. For consistency and convenience in comparison of the published information, the deoxidation product as referred to the following reaction is expressed in terms of the percentage by weight of silicon and oxygen in the melt in equilibrium with solid silica: SiO (s) = Si + 2 O; K'l = [% Si] [% 012 [I] Theoretical attempts to calculate the deoxidation constant for silicon in liquid iron from the free energies of various reactions yielded results which were invariably lower than the experimental values. Thus, the deoxidation "constants" calculated by McCance,1,2 Feild,3 Schenck, and Chipman were of the order of 10, which is below the experimental values by a factor of more than 10. Experiments of Herty and coworkers" in the laboratory and steel plant resulted in an average deoxidation constant of 0.82x10 ' at about 1600°C. The technique employed in their investigation was crude and the reported temperature was quite uncertain. The concentration of silicon was obtained by subtracting silicon in the inclusions from the total. Since at least some of the inclusions resulting from chilling must represent a fraction of the silicon in solution at high temperatures, such a subtraction is not justifiable. Results of Schenck4 for K'1 from acid open-hearth plant data yielded a value of 2.8x10-5, which was later revised as 1.24x10 at 1600°C. Similarly Schenck and Bruggemann7 obtained 1.76x10-5 at 1600OC. The discrepancies and errors involved in the acid open-hearth plant data as compared with the results of more reliable laboratory techniques were attributed by these authors to the lack of equilibrium and the impurities in liquid metal and slag, and are sufficiently discussed elsewhere." Korber and Oelsen" investigated the relation between dissolved oxygen and silicon in liquid iron covered with silica-saturated slags containing varying concentrations of MnO and FeO. The deoxidation products obtained by their method scatter considerably, and their chosen average values of 1.34x10, 3.6x10-5, and 10.6x10-5 1550°, 1600°, and 1650°C, respectively, represent the best experimental results which were available until quite recently. Darken's10 plant data from a steel bath agree approximately with their data at 1575° to 1625°C. Zapffe and Sims" investigated the reaction of H2O and H2 with liquid iron containing less than 1 pct Si and obtained deoxidation products varying by a factor of more than 20. Inadequate gas-metal contact and lack of stirring in the metal bath should require a longer period of time than the 1 to 5.5 hr which they allowed for the attainment of equilibrium. Furthermore, their oxygen analyses were incomplete and irregular and confined to a few unsatisfactory preliminary samples. Their results did indeed indicate that the activity coefficient of oxygen is decreased by the presence of silicon, although they made no such simple statement. They chose to attempt to account for their anomalous data by the unlikely hypothesis that SiO is dissolved in the melt. Hilty and Crafts" investigated the reaction of liquid iron with acid slags under an atmosphere of argon, making careful determinations of silicon and oxygen contents at several temperatures. Despite erroneous interpretation of the data at very low silicon concentrations, their data represent the most dependable information on this equilibrium that has been published. In the range 0.1 to 1.0 pct Si, their data yield the following values for the deoxidation product: 1.6x10-5, 3.0x10- ', and 5.3x10 at 1550°, 1600°, and 1650°C, respectively. The purpose of the work described herein was to study the equilibrium represented by eq 1 as well as the following reactions, all in the presence of solid silica: SiO2 (s) + 2H2 (g) = Si + 2H2O (g);

Jan 1, 1953

The following correspondence relating to a paper bearing the above title, presented by J. F. Wolff, at the New York meeting in February, 1917, and published in the Transactions, Volume LVI, page 142, has passed between the author of the paper, and Mr. Anson G. Betts, and is interesting, although it was received much too late for incorporation in its proper place in Volume LVI. ANSON CT. BETTS, Asheville, N. C.-1. I should like to ask Mr. Wolff if he finds-from analysis of the iron formation and of the iron ore, and from the relative amounts of each in each unit area of the formation, unleached and after leaching, that the iron remains entirely insoluble and the total quantity still remains present; or whether he finds that some of the iron is removed, or possibly even added by deposition from the water passing through the formation. 2. The water that passed into the iron formation had to go somewhere; was it absorbed by underlying formations through hydration, or, after passing through the ore formation, did it come to the surface in springs at a lower elevation, or how did it escape from the ground? 3. I should like to ask Mr. Wolff whether he finds that the iron formation in the sedimentary series does not, come next to the quartzites and generally between the quartzites and slates. J. F. WOLFF, Duluth, Minn.-1. In common with others, you appear to have some hesitancy in accepting the fact of the removal, by solution, of the enormous quantity of silica which has been leached out of portions of the Biwabik iron formation, thus forming orebodies of merchantable iron ore. I believe that even Dr. Waldemar Lindgren once hesitated to accept this fact. However, the evidence is so simple and absolutely conclusive that the fact is established beyond all question. At the contact of orebodies with their rock walls, the bands of iron ore in the orebody can be seen in contact with the corresponding bands of original iron oxide in the rock wall, and the chert layers in the rock wall can be seen to give place to fine granular material (fine silica and iron oxide) and pore space. This is especially noticeable where slumping at the rock walls his not been so great as to displace the layers in the orebody from their contact with their corresponding layers in the rock wall.

Jan 9, 1918

By E. O. Kirkendall

THE investigation reported herein was undertaken to obtain data to supplement those presented in an earlier paper,' particularly for longer times at a higher temperature. This information may further develop our knowledge of the mechanism of diffusion in substitutional solid solutions. Diffusion of solute atoms interstitially dissolved is not difficult to visualize; it can take place without much disturbance of the solvent atoms. The mechanism of diffusion of solute atoms substitutionally dissolved is not so easily understood. Many theories have been advanced. Rosenhain,2.3 Frenkel,4 Smekal,5 Langmuir,3,6 Steigman, Shockley and Nix,7 and Johnson8 all proposed theories to explain diffusion. Langmuir's proposed mechanism consisted of a simple cyclic interchange of atoms involving an interchange in lattice positions of four or more atoms. This mechanism, accepted by the author at the time of his previous publication,' and apparently quite generally accepted, required a net exchange in positions of both solute and solvent atoms in equal numbers. In other words, the rate of diffusion of the solvent and solute atoms would be the same. That this cyclic interchange in lattice positions of solute and solvent atoms in equal numbers is the only true mechanism of diffusion is denied by the evidence presented in this paper. EXPERIMENTAL PROCEDURE This modification of similar procedure1 will be outlined briefly. The method consisted of the following steps: I. A pure Muntz metal (60.6 per cent Cu, 0.1 per cent total impurities) that was almost all beta brass at 780°C. was chosen. 2. The brass was turned between centers in a lathe to a diameter of 0.5965 inches. 3. After the brass was cleaned, it was electroplated with pure copper to a diameter of about one inch. 4. The sample was heated slowly to 400°C. under reduced pressure and held at that temperature for 4 hr. to remove occluded gases. It was then cooled to room temperature. 5. The sample was heated to 780°C. ±3°C. and held at that temperature for different lengths of time; then quenched. Samples were cut off each time after quenching. Metallographic samples 34 in. thick were removed at I hr., 6 hr., 24 hr., 96 hr. and 701 hr. After 96 and 701 hr. samples of about I in. were removed for X-ray analysis. 6. The metallographic samples were polished on the cross section and photo-micrographs were taken. 7. The I-in. samples were polished and etched on both ends. With the aid of a microscope each was carefully mounted in a four-jaw chuck in a lathe, so that they could be accurately bored for an arbor. 8. Turnings were taken for each X-ray sample. After each set of turnings, the sample was heated in an oil bath for about 3a hr. at 300°C. It was then etched in 25

Jan 1, 1942

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates are required for certain end uses, and these are produced from smaller colemanite-ulexite-probertite bodies. Sodium-free borate compounds also are produced from boric acid, which can be manufactured from either sodium or nonsodium borate minerals. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of over a million tons of B2O3. Leadership in supplying borates shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates, In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, CA is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, CA, the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "10-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7 • 10H2O. In addition to ship¬ping all major refined borate products from [ ]

Jan 1, 1983

By Edmund Kirby

This meeting marks the point at which the long-standing dissatisfaction with the mineral-land laves, the innumerable protests against them, and the many isolated efforts to obtain relief, have developed into a general movement for the: revision. That part of the mining industry which is affected by these laws has three general organizations to speak for it: the American Institute of Mining Engineers, Mining and Metallurgical Society of America, and the American "A Mining Congress: all of which are represented in this meeting. In the series of able and thoughtful presented here, prominent men have discussed the evils of the present laws aid some of the reforms which should be made in them. We all appreciate fully the ultimate value of these studies; but we are also painfully aware of the fact that discussion of this kind has been going on for a quarter of a century without any other effect than a steady increase in the mass of printed records stored on library shelves. In order to get any practical result we must induce an indifferent government at Washington to act, and to do this we must unite in pushing some practical plan whereby it may act in a simple and effective way and with the least possible amount of criticism or opposition. The actual question before us is not whether the mining laws are bad; for their evils and absurdities are not only beyond discussion but also beyond the resources of a temperate and dignified vocabulary. It is not what particular changes ought to be made; for it is premature to make specific recommendations until there is some one to listen to them. Moreover, we all know that there are wisdom and experience enough available, and awaiting that time, for the creation of a code which would be a model to the mining world. The practical question now is, how to obtain the revision; and since the American Mining Congress has of late restricted its attention to this phase of the problem I wish as one of its representatives here to present its views upon the matter.

Jan 6, 1914

By A. Taylor

IN a previous communication,l the quaternary system Ni-Cr-Ti-A1 was described in detail and it was shown how certain alloys used for high-temperature applications could be construed as consisting of Ni,Cr suitably modified by the addition of aluminum and titanium in relatively small amounts. With the correct aging treatment, the ordered face-centered-cubic Berthollide phase, y'-Ni,Al, could be precipitated from the face-centered-cubic primary y-solid solution. By increasing the proportion of titanium with respect to aluminum, it was also possible to precipitate the very brittle hexagonal-close-packed Daltonide phase, ?-Ni,Ti. From the nature of the system it seems reasonable to expect the y and y'-phases to take appreciable amounts of cobalt and iron into solid solution. In the case of the present investigation it was decided to confine the work to iron additions only. This element may be introduced in two quite distinct ways: 1) as a simple replacement for nickel; and 2) as a replacement for chromium, titanium, and aluminum. The second method of iron addition forms the basis of the present investigation, which is, in effect, a study of the pseudo-quaternary system Ni,Cr-NiPe-Ni,Ti-NLAl. For purposes of reference, Figs. 1, 2, and 3 have been included and illustrate the quaternary system Ni-Cr-Ti-A1 described in the previous paper along with sections through N&Cr-Ni,Ti-Ni,Al at 750" and 1000 "C respectively. As will be shown below, the pseudo-quaternary system with components Ni,Cr, NiPe, Ni,Ti, Nihl is remarkably similar in many ways to the face defined by Ni,Cr-Ni,Ti-Ni,Al because of iron re-

Jan 1, 1958

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By W. L. Austin

The advance made in recent times in this branch of metallurgy is indicated by the attention the subject is receiving from important American copper-producing companies. Reference to the files of publications devoted to the mining industry discloses that some 20 American companies are actively investigating the amenability of their ore, or other material, to leaching methods, and that plants of varying capacities up to 10,000 tons per day arc under construction or are projected. Several leaching works are in commercial operation. It has been frequently pointed out that no method of leaching is universally applicable, for the reason that each ore differs in some particular from apparently similar ore found elsewhere, and also because local conditions are rarely the same even where the ore closely approximates in character that being worked at some other point. For this reason the older companies are approaching the matter in a conservative manner, experimentally determining for themselves the salient features in each instance. In considering a leaching proposition three factors at once fix the attention: (1) disengaging the metal from mineralized forms in which it is found in nature; (2) recovering the metal in a commercial state after it has been dissolved; (3) the apparatus best adapted to carrying out the several operations. Bringing the Metal into Solution This feature.has been found to present no serious difficulties. Numerous solvents for copper are known, and it has been repeatedly demonstrated on a commercial scale that from 80 to 90 per cent. of the metal contained in an ore can be rapidly brought into solution. It is interesting to note, however, that all of the companies above referred to have selected sulphuric acid as the basis for a lixiviant. Where oxidized ore practically free from precious metals is treated simple leaching with

Jan 1, 1915

By M. H. Cullender

The performance characteristics 01 gas wells producing from formations which fail to stabilize within a relatively short period of time are obscured by the interrelation of the coefficient (C) and the slope "n" of the conventional back-pressure curve q = C(P2 f- p2s)n An empirical method is presented whereby the characteristic or true slope (11) of the back-pressure curve may be determined for a particular gas well. For those gas wells which do not stabilize within a relatively short period of time, the coefficient (C) is considered as a variable with respect to time and as a constant only with respect to a specific time. Thus, the back-presrure performance of such a well is presented as a series of parallel curve5, each curve representing the performance of the well at the end of a given time interval. Through use of the method presented, a simple presture gradient is developed and maintained within the drainage area around a producing gas well during the test period in order that the variation of the coefficient (C) with respect to time does not obscure the true value of the lope. INTRODUCTION The back-pressure method of testing gas wells as set forth by Schellhardt and Rawlins1 is dependent upon the requirement that a series of flow rates and corresponding pressure data be obtained under stabilized conditions. These data arc then plotted on logarithmic coordinates of flow rate (Q) vs difference in squared pressures (P2f — P2s) in order to determine the constants (C) and (n) for Equation 1. With respect to this method of presenting the performance characteristics of a gas well, it should be pointed out that although Equation 1 is an empirical relationship, the form of the equation was justified to a considerable extent by an independent development by Muskat and Botset.2 This development was theoretical in nature; however, certain assumptions with respect to the type of flow existing (viscous vs non-viscous) were madc which may or may not be correct. As the use of the method presented by Schellhardt and Rawlins spread through the industry, it became evident that the method of testing was applicable for those wells which approached stabilized prbducing conditions within a relatively short period of time. Performance characteristics could not be determined by this method, however, for wells which approached stabilized protlucing conditions slowly over a considerable period of time. This characteristic of "slow stabilization" has generally been associated with gas wells producing frorn reservoirs of low permeability. As the demand for natural gas continued to grow through the years, a great number of wells were completed in reservoirs of low permeability which exhibited "slow stabiliz:~tion" characteristics. Consequently, the problem of determining the true performancc characteristics of these wells became more apparent. It is with this problem in mind that the isochronal performance method of determining the flow characteristics of gas wells is presented.

Jan 1, 1956

By W. R. Crane

MINING of the red iron ores of the Birmingham district has been carried on energetically during the past 50, years, and their development has created a large iron and steel manufacturing, center, the only important one in the South. The district produces approximately 10 per cent. of all the iron ore of the United States (80 per cent. of the Alabama ore mined is red ore) ; also, 43 of the 419 blast furnaces of the country are in the district tributary to Birmingham. The rapid growth of the district has been made possible through investigations that resulted in radical changes in furnace practice, and a still greater impetus will come from the study of the low-grade, high-silica ores, as a result of which they will be made amenable to treatment by concentration. Mining practice in this district has been comparatively simple because of the occurrence of the ore; but with the-rapid extension of the work-ings and the disturbed condition of the ore bed at some distance from the outcrop, more difficult conditions are encountered and the tendency is toward worse rather than better conditions. Should the high-silica ores of the lower bench of the Big Seam become available through beneficiation, mining practice will have to be modified to meet the new conditions, which will be rendered more difficult by the increased weight of cover that will exist at considerable distances from the outcrop. Support of workings will require greater attention and the efficient and economical operation of the mines will depend largely on the successful solution of the problems of working-and handling the ore.

Jan 9, 1924

By T. W. Guy

DuRing recent years, tremendous strides have been made in the economical use of coal. This has resulted in, and to some extent has been a result of, making the fuel specifications more and more rigid. For this reason, all producers have found it necessary to improve their preparation materially, both as to sizing and the elimination of impurities, either by more effective preparation underground or at the tipple and cleaning plant, or both. This cause and its effect in all producing fields seem likely to continue for several years at least. The splendid inherent qualities of the Pocahontas and New River coals are known all over the world, but their good reputation is only partly due to inherent qualities, and to natural conditions which generally favor loading coal comparatively free from impurities; it is due in large measure to the care and skill used, either with or without the aid of mechanical devices, to ship products consistently low in ash. The first coal from the West Virginia smokeless fields was mined and shipped near Quinnimont, on New River, in 1871, while the first shipments from the Pocahontas field were in 1883. The development of both fields progressed rapidly. At first activities followed the main lines of the Chesapeake & Ohio and Norfolk & Western railroads, and were extended later as branch lines were built from these roads. The Virginian R. R., about 1907, opened up the Winding Gulf territory, which has since become a large producer of smokeless coals from the Pocahontas and the New River measures. Early Cleaning Methods In the early days, the tipples were simple wooden structures, with bar screens for separating the fines from the lump coal. All cleaning was done by the miners at the face, or by pickers in the railroad cars. Gates were provided in the chutes by which the flow of coal could be stopped when necessary while the pickers raked the surface of the coal in the car and picked out the impurities. A large percentage of the fine coal or slack was used for making coke at the mines in beehive ovens. The

Jan 1, 1932

By M. A. El-Aouar

Drilling muds are complex colloidal systems. In an effort to analyze the physical properties that affect their performance at high temperature, an investigation was made of the hydrothermal stability of the monoionic hydrogen, calcium and magnesium forms of montmorillonite and attapulgite. Samples were heated to 400°1F in a simple autoclave and analyzed for cation exchange capacity, c-axis X-ray diffraction spacing and pH factor us sodium hydroxide titration dependence. Out of the six monoionic clay minerals tested, calcium montmorillonite and magnesium attapulgite showed the least base exchange capacities and were relatively unaffected to heat. It is concluded that, of the six clays studied, these two clays were the most suitable forms for use in drilling fluids. INTRODUCTION The drilling of deep wells is dependent upon the drilling mud, and problems frequently arise concerning the effect of mud temperature and prolonged heating. Drilling muds are complex colloidal systems. In an effort to analyze their behavior in deep, hot boreholes, it was thought desirable in this investigation to study suspension of pure, monoionic montmorillonite and attapulgite clays before and after hydrothermal heating. Chemically, clays are hydrated aluminum silicates, such as montmorillonites and attapulgites. The structure of montmorillonite is composed of units made up of two silica tetrahedral sheets with a central alumina octahedral sheet. Attapulgite consists of double silica chains running parallel to the c-axis with the chains linked together at their longitudinal edges. The apexes of the tetrahedrons in successive chains point in opposite direc-tions.4,7,10 One of the most important characteristics of clay minerals is their property of sorbing certain anions and cations and retaining them in exchangeable state. The property of exchange capacity is measured in terms of milliequivalents (meq) per 100 gm of clay. The cation-exchange capacities are taken at pH 7 from titration curves which show the relation between pH and milliequivalents of added NaoH.9,11 The following are causes of cation exchange: (1) broken bonds around the edges of the silica alumina units would give rise to unsatisfied charges, which would be balanced by adsorbed cations; (2) substitution within the lattice structure of trivalent aluminum for quadrivalent silicon in the tetrahedral sheet and of ions of lower valence; and (3) the hydrogen of exposed hydroxyls may be replaced by a cation which would be exchangeable. The primary techniques employed to study the effects of hydrothermal treatment were titration curves and X-ray diffraction analyses. Titration curves were useful in characterizing the nature of the clay mineral surface and the stability of the various samples to attack by acid or alkali before and after hydrothermal treatment. X-ray diffraction analyses were used to determine changes in the nature and crystal structure of the minerals present and to determine the cations in exchange positions on the montmorillonite samples. EXPERMENTAL PROCEDURE PREPARATION OF SAMPLES Selected samples of Wyoming bentonite and attapulgite clay from mines along the Georgia and Florida border were purified by centrifugation to remove all particles larger than 2 microns. In preparing magnesium attapulgite, first a 1.00-normal solution of magnesium acetate was prepared. The pH of the solution was adjusted to 7.0 by adding magnesium oxide. One hundred grams of attapulgite clay were mixed in a blender for 30 minutes with the magnesium acetate solution. The attapulgite solution was left overnight, and then filtered in a Buchner funnel. The suspension was leached with further quantity of magnesium acetate solution and then washed with distilled water for 20 days, after which the filtrate was free from magnesium ions. The concentration of magnesium attapulgite in the clay slurry was adjusted and determined quantita-

By Thomas H. Sheldon

In the zeal for opening up new ore-bodies, or for extracting the ore from attractive bodies already opened up, we very often lose sight of the fact, that, after all, the operation of a mine is a business proposition, pure and simple, and, for the best working-results, should be treated upon a strict business basis. Of course, in every mine of consequence, a record is kept of expenditures and receipts, and such glittering generalities as " gross receipts," " net receipts," " mining expenses," and a per cent. profit," can be told to the cent; but does this record show economy of management, as compared either with the same record of other months, or with the record of other mines of the same class ? Moreover, if such a record shows that the cost of mining is high, does it in any way enable the manager to put his finger on the leakage ? Does it necessarily follow that a mine which makes a profit of, say, 40 per cent. on 25-dollar ore, is doing less economical mining than one which saves 60 per cent. on 80-dollar ore ? Of course the figures in the latter case look the more attractive; yet when it comes to the point of saving everything which can be saved, and of cutting down expenses to the lowest possible cost of operation, the former mine is doubtless on the firmer and more economical financial basis. But as to the relative merits of the system of mining in the two cases, nothing could be decided without a basis of detailed comparison ; if one system is more economical than the other, why is it so, and wherein does the advantage lie ? This can be shown only by keeping accurately the cost of each mining operation. And no matter how dissimilar two mines may be in character and operation, yet there are a few general heads common to all mining operations. In the first place, it is necessary to break the ore from the solid ground;

Jan 1, 1907

By N. J. Grant, A. W. Mullendore, Y. Ishida

Creep tests were performed at 500°F on polished specimens of A1-3 pct Cu at stresses of 2000, 4000, and 6000 psi. The effects of the size and distnbution of the second phase were studied in connection with the mechanisms of deformation, especially grain boundary sliding. Although the amount of grain boundary sliding varied considerably for the different heat treatments, yestriction of grain boundary sliding is not due primarily to precipitate on the grain boundary. NUMEROUS prior investigations of grain boundary sliding, notably those of McLean, 1 Rachinger, 2 Rhines, Bond, and Kissel, 3 and Brunner and Grant,4 have established the importance of this phenomenon in the deformation of pure aluminum and its solid-solution alloys at elevated temperatures. An extension of this kind of study to the case of a simple two-phase structure is an important step towards understanding the deformation behavior of more complex alloys. A two-phase A1-3 pct Cu alloy was selected for this study. The creep behavior of alloys in this system has been studied by Sully and Hardy,5 by Underwood, Marsh, and Manning,' and by Pelloux, Chaudhuri, and Grant.7 In these studies, the prior heat treatments were such that some precipitation took place during the tests in most cases. Pelloux, Chaudhuri, and Grant7 studied the creep of A1-2 and 3 pct Cu alloys in the overaged condition. Their results indicated that the structure most effective in promoting high-temperature strength consisted of a fine, closely spaced grain precipitate and large, widely spaced particles on the grain boundary. The present work consists of quantitative meas- urements of grain boundary sliding during creep of an A1-3 pct CU alloy with four different precipitate distributions. The aims were to quantitatively define the role of the second phase on grain boundary sliding, and to obtain information regarding the mechanism of grain boundary sliding. MATERIALS AND PROCEDURE A high-purity A1-3 pct Cu alloy, kindly supplied by Alcoa, was used in this investigation. The composition of the alloy in weight percent was as shown in Table I. This composition is such that A12Cu exists as a second phase at temperatures below 850°F. A homogeneous grain size of 0.6 to 0.8 mm was obtained by annealing the machined test bars for 5 min at 1000°F, furnace cooling to 930°F, and homogenizing for 5 hr. Following the recrystalli-zation and homogenizing anneal, four different heat treatments shown in Fig. 1 were utilized. The F7 and F5 treatments utilize a furnace cool to the aging temperature while Q7 and Q5 have a water quench from the homogenization temperature before aging. Figs. 2 to 5, and Table 11, show the size and shape of precipitate dispersions obtained with the above heat treatments. The heat treatments produce variations in the dispersion both in the grains and along the grain boundaries. Precipitate particles along the grain boundaries are rounded and large (about 1.5 p diameter) in the F5 and F7 structures (Figs. 3 and 5). The grain boundary precipitate was somewhat smaller (0.9 p diameter) in the Q7 structure and no grain boundary precipitate was detected in the Q5 structure using light microscopy. The pre-

Jan 1, 1964

By D. Roberts

SUMMARY In order to accommodate a new plant in a limestone quarry in the Mendip Hills, it became necessary to excavate a potentially unstable disused face of the quarry. A simple two-dimensional graphical method was used to analyse a failure, which occurred during a period of exceptionally heavy rain in 1968, and the results of this analysis were used in estimating the stability of the proposed excavation. The presence of water in vertical fissures and tension cracks was found to be a dominant factor in determining the stability of these faces. The results of this approximate analysis were used as a guide in deciding upon the final slope design and the purpose of presenting this example is to illustrate how the various factors involved in arriving at this design were weighed to arrive at a compromise between theoretical recommendations and practical considerations. INTRODUCTION The successful outcome of a geological and geochemical survey to prove adequate re- serves of high quality limestone, suitable for producing burnt lime, led to planning for the installation of the necessary plant at Amalgamated Roadstone Corporation's Batts Combe Quarry at Cheddar in Somerset. Topographic and property boundary limits added to restrictions which were likely to be imposed by any forthcoming planning consents and restricted the choice of plant location to one site. The particular site is, in fact, the main floor area of the original quarry which, like many hillside quarries, had been worked with just one face. Before a benching scheme had been introduced on higher ground, the original face had attained a height of 230 ft. and sloped at angles of 58º to 64º. Fig. I shows the present configuration of the disused quarry face and the present working area above. The floor area below the disused face accommodates the existing crushing, conveying, and screening plant. The new facilities for lime burning are to be in addition to the existing main line business of producing roadstone and concrete aggregates and, although a new aggregate production plant would be included in the new installation, no disturbance of current production was to be contemplated.

Jan 1, 1972

By Arthur O. Gates

RittingeR's law of the energy expended in crushing is, as roughly stated by Profcssor Richards,' that the work of crushing is proportional to the reduction in diameter; or, as I have more fully expressed it: "The work done in crushing is proportional to the surface exposed by the operation; or, better expressed for this purpose, the work done on a given mass of rock is proportional to the reciprocal of the diameter of the final product—assuming that all the mass has been reduced to one exact sine, which is only theoretically possible."² Kick's law is stated by H. Stadler as follows :3 "The energy required for producing analogous changes of configuration of geometrically similar bodies of equal technological state varies as the volumes or weights of these bodies." In other words, the energy expended is proportional to the volume reduction, instead of the diameter reduction. That these two laws would give widely different results may be shown by a simple imaginary case. A ton of 16-in. cubes is broken to 1-in. cubes at the first operation, and these are broken to 1/16. cubes at a second operation. Since the first operation produces only one-sixteenth as much new surface as the second, the ratio of energy expended in the two operations would be by Rittinger's law as 1 to 16. By Kick's law, since the volume-reduction ratio is the same in both cases, the ratio of energy would be 1 to 1. This discrepancy is great enough to challenge a test by actual experiment, of which there has been, hitherto, but little compared with the amount of argument. The present paper is the record

Jan 1, 1916