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By W. M. Robertson

The formation of grain boundary grooves on surfaces of poly crystalline samples of cobalt and iron immersed in liquid lead has been studied. The grooves form by volume diffusion of the solutes cobalt and iron in the liquid. The diffusion coefficients of the solutes in liquid lead are derived from the measured rate of grooving. The diffusion coefficients are described by the relation D = Do exp (-Q/RT), with, for cobalt, Do = 4.6 x 10-4 sq cm per sec and Q = 5300 ± 800 cal per mole, and for iron, DO = 4.9 x 10-3 sq cm per sec and Q = 10,500 ± 1500 cal per mole. LIQUID metal-solid metal interactions occur at solid-liquid interfaces. Interfacial energy provides a driving force to change the morphology of the interface. Mullins1,2 has derived expressions for the kinetics of interface morphology changes driven by capillarity. These expressions can be applied to an isothermal system of a solid in equilibrium with a liquid saturated with the solid. Surface profile changes can occur by volume diffusion of the solute in the liquid, by volume self-diffusion in the solid, and by interfacial diffusion at the liquid-solid interface. A groove will form at the intersection of a grain boundary with a solid-liquid interface, reducing the total interfacial free energy of the system. The solid-liquid interfacial energy ? must be greater than half the grain boundary energy of the solid ?6 for Mullins' calculations to apply. If ? is less than ?b/2, then the liquid penetrates the boundaries, separating the grains rather than forming grooves. Boundary penetration did not occur in the work described here. where CO is the equilibrium volume concentration of the solid in the liquid, Dv the volume diffusion coefficient of the solid in the liquid, ? the interfacial free energy of the solid-liquid interface, O the atomic volume of the solid crystal, k Boltzmann's constant and T the absolute temperature. Eqs. [1] and [2 ] also apply to grooving by volume self-diffusion in the solid,1 with CoODv = D Self, where DSelf is the volume self-diffusion coefficient of the solid. For a grooving mechanism of interfacial diffusion at the solid-liquid interface, the groove width is given by2 where CS is the interfacial concentration of the diffusing species, and DS is the interfacial diffusion coefficient. Eqs. [1] and [3] can be used to determine the mechanism of groove growth. A t1/3 dependence of the growth indicates volume diffusion and t1/4 indicates interfacial diffusion. In some cases, volume diffusion and interfacial diffusion both can contribute substantially to the grooving process, causing the time dependence to be intermediate between t 1/3 and t1/4.3 For these cases, the relative contributions of the two processes can be separated.4 However, in many cases, one process will be dominant, and the data can be analyzed on the basis of Eq. [1] or Eq. [3] alone. The time dependences for volume diffusion in a liquid and volume self-diffusion in a solid are the same. However, the self-diffusion contribution of the solid is usually negligible compared to volume diffusion in the liquid. After the grooving mechanism has been determined, Eq. [1] or Eq. [3 ] yields the kinetic parameter A or B. The kinetic parameter can be used to calculate values for the unknown quantities in the product CD?. Usually C is known or can be estimated. If ? is known, then D can be calculated. In a measurement of grain boundary grooving of copper in liquid lead,' the time dependence indicated volume diffusion in the liquid. The quantities Co, Dv, and ? were obtained from the literature, giving excellent agreement between the observed values of A and the values calculated from Eq. [2 ].5 In a study of the grooving of several refractory metals in liquid tin and liquid silver, A1len6 educed that grooves formed by volume diffusion in the liquid. In a study of nickel in a nickel sulfide melt, Steidel, Li, and spencer7 found volume diffusion grooving kinetics. Both Dv and ? were unknown, so they could not obtain either one separately, though they did obtain a reasonable value for the temperature dependence of the product Dv ?. Several methods have been used to obtain surface profiles. It can be done by sectioning through the interface7 or by chemically removing the liquid from the solid surface after solidification of the liquid.6 However, if the liquid dewets the solid on removing the solid from the melt, then the interface can be observed directly. This method was used previously' and was utilized also in the present study. EXPERIMENTAL PROCEDURE Lead of 99.999 pct purity was obtained from American Smelting and Refining Co. Cobalt sheet was obtained from Sherritt-Gordon Mines, Ltd., with a nominal purity of 99.9 pct, the principal impurities being nickel, iron, copper, carbon, and sulfur. The sheet was

Jan 1, 1969

By D. W. Hutchinson, W. W. Wen, A. A. Terchick, J. C. Anderson

It is estimated that approximately 3% of the raw coal processed today in coal preparation plants throughout the nation will ultimately report to slurry-tailing disposal (Anderson, 1975). The usual disposal method is to pump refuse slurry containing - 48 mesh (300 pm) refuse into dams or impoundments constructed of coarse refuse. The failure of an impoundment at Buffalo Creek, Saunders, WV (Anon., 1972) resulted in an evaluation of refuse disposal methods by various regulatory agencies as well as coal producers. The result of this evaluation was the promulgation of federal regulations dealing with the construction, operation, and final abandonment of coal refuse disposal area. As a consequence of these regulations, the use of the landfill/impoundment method of disposal became in some cases economically unfeasible or technically impossible. US Steel has studied a number of alternative methods of refuse disposal. During an investigation of mechanical dewatering with a pressure filter, portland cement was added to the slurry to solidify the filter cake. Because of the success of the cement addition, it was decided to study the stabilization of fine coal refuse slurry through use of cement-type additives. The goal of the investigation is to develop a process that will use cement-type additives to solidify the refuse slurry into a form that can be handled and stacked with the coarse refuse, thus eliminating the need for slurry impoundments.

Jan 1, 1982

By J. P. Savely, D. E. Nicholas, R. D. Call

Progress in the technology of slope design over the past 15 years now permits the selection of rational slope angles if suitable data on geology, hydrology, and rock properties are available for a specified project. Although a full-scale slope design study remains the best course of action, there are situations where an extensive study is not feasible due to time or budget constraints. Two typical examples are: (a) selecting pit slope angles for a preliminary feasibility study at the exploration stage; and (b) coping with a slope failure in an operating mine. In both instances, slope angles must often be chosen on the basis of data that are currently available or can be readily obtained. All too often during exploration programs, a feasibility study is initiated shortly before the decision deadline to drop the property or proceed to purchase. If the only existing data at this point are a few cross-sections at odd angles showing ore and waste contacts or a dog-eared map of the surface geology, there may not be time to collect and organize sufficient information for the design of slope angles. On the other hand, if during the drilling program geologic cross-sections were constructed and the structural data compiled in tabular form, rational slope angles could be computed within the allotted time.

Jan 4, 1977

Discussion of the paper of COURTENAY DEKALB, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 331 to 337. HORACE V. WINCHELL, Minneapolis, Minn.-Mr. Dehalb summarizes the reasons which he believes are important for the revision of the mining laws, as follows: "1. The conceptions as to the characteristics of orebodies that were held at the time the statute of 1872 was enacted have since proved to be in many respects erroneous." We all appreciate the force of that suggestion. The idea of the old prospector who made rules and regulations in the early days, which were attempted to he incorporated, so far as possible, in the Mining Act of 1872, was that all of the veins in a certain district outcropped upon the surface, or approximately parallel to each other upon the surface, and maintained that parallelism beneath the surface. Therefore, it seemed perfectly proper and natural for each man to stake his claim upon an outcropping, and have the right to follow that vein in working downward, with the general expectation that his workings would always remain just as far away from those of his neighbor as the outcroppings upon the surface. This does not happen to be the case. Dr. Raymond has very ingeniously referred to the subject in one case, in words which read as follows: "If all mining properties presented this beautiful simplicity of structure (ideal location of ideal vein), and all mining locators exhibited a corresponding simplicity of purpose, the application of the law would be easy, but the naiveté of the statute fares badly between the freaks of nature and the tricks of man."

Jan 5, 1915

By James T. B. Ives

The map exhibited* as an example of my method of construct ing geological strata-maps is essentially an educational appliance. The method, however, is available for the production of maps of comparatively small areas, which, I am confident, will be found of great practical value to mining engineers. Before stating how the method may be so applied I will briefly describe the map exhibited, as the easiest way of making my meaning clear. Almost any region might be taken. This map represents the eastern half of the United States; and the geology is that of the map issued by the Geological Survey, and revised and extended subsequently by Professor Hitchcock for your Institute. I use ten cards, of the colors used in the geological map, each having the geog raphy of the area printed upon it; and I superimpose these in the order in which the colors occur in the index to the map. I next cut away a portion of each card, excepting the lowest, leaving only so much of each as represents the exposure of the formation of that color plus all those which overlie it. When that is done, the whole, looked at from a distance, appears to be an ordinary geological map. Looked at more closely, however, the formations are seen to overlie one another, as in nature. The cards are covered with glass in a frame, which, hinged at the bottom edge, can be let down. The cards are then found to be all hinged in the same manner, and they, too, may be lowered, one after the-other. I am told by teachers of geology of great experience and the highest reputation that by this appliance they will be assisted in im parting to students the first facts and principles of geological sci ence. Having let down the whole series of cards, until that repre senting the Archaean is seen underlying all the rest, the teacher will gradually rebuild it. The Cambrian will thus be laid down upon the Archaean before the eyes of the class, the Silurian upon that,

Jan 1, 1888

By J. Randel Hill

The 64th Texas Legislature passed the "Texas Surface Mining and Reclamation Act," Chapter 131, Texas Natural Resources Code (subsequently referred to as "the Act"), at a point in time when little surface mining had taken place within the state. Thus, enactment of regulatory control governing mining operations in our state has, for the most part, preceded widespread, intensive mining activity. I should point out that the statute applies only to the extraction of coal, lignite, uranium and uranium ore. A recent opinion rendered by the Attorney General's office has stated that extraction of the named elements, when it occurs incidental to the extraction of other materials, e.g., clay, is not not an activity subject to the Act. An important theme of the Act, frequently overlooked in other environmentally oriented legislation, is recognition of the Act's affect on the mining industry. The Act states that "the extraction of minerals by surface mining operations is a basic and essential activity making an important contribution to the economic well-being of the state and nation" and, in reference to reclamation being accomplished contemporaneously with mining, provides a recognition that "the extraction of minerals by responsible mining operations is an essential and beneficial economic activity." This legislative recognition is, of course balanced against the need for proper mined land reclamation, the rights of surface owners, the need to guard against unreasonable degradation to land and water resources and numerous other actions or events that the Legislature wanted protected. Another rather pervasive general theme that is established in the Act is the concept that the agency is entitled to obtain whatever information, or take whatever action, that appears reasonably necessary to effectuate the purposes of the Act. This concept, coupled with the detailed requirements placed on mining operations in the portions of the Act dealing with Permit Applications, Reclamation Plan and Reclamation Standards, easily insures that surface mining activities can and will be regulated to the extent necessary. Section 131.102(b)(2) is probably the most relevant provision in the Act which deals with the preclusion of mined lands becoming waste lands. This portion of the Act states that the surface mining operator shall: ". . . restore the land affected to the same or a substantially beneficial condition. ." In this language the Legislature had made it abundantly clear that the abandoned or orphaned lands found in some of the Eastern states, will not be tolerated in this State, and provided the Commission with a degree of latitude to determine what condition would be appropriate in each individual mining situation. I bring this area of the Act to your attention because it is the area which has received the most inquiries and concern by operators, i.e. what does "substantially beneficial" constitute? The Commission's staff has spent a considerable amount of time wrestling with the statutory language "substantially beneficial" to determine the legislative intent and provide operators with guidance of what they can expect. In this regard, the most definitive criteria in our opinion lies in the Act's legislative hsitory. The Legislature had before it basically three reclamation standards namely: House Bill 656, considered to provide the most stringent reclamation standard and identical to Senate Bill 66; House Bill 1717 which was supported by industry spokesmen and was considered to contain the least stringent reclamation standard; and Senate Bill 55 which was adopted by the Legislature. During the Bill's initial hearing before the House Environmental Affairs Committee, the House sponsor of the Senate Bill 55, which was the Bill eventually adopted, made the following statement: (I am quoting verbatim from the Committee's transcript although substituting the speaker's reference to the authors names with the Bill's numbers.) "An example of the differing approaches of the four bills can be seen in the area of reclamation standards and this is critical. House Bill 656, talking about restoring the surface of the land, House Bill 656 has this statement: 'At least fully capable of supporting the use to which it was capable of supporting prior to any mining or any higher or better use.' In other words you have to restore it to the level it was prior to the mining. Senate Bill 55: 'Restore the land to the same or substantially beneficial use.' Substantially beneficial use. (Emphasis his) House Bill 1717 says: 'Restore insofar as practical to appropriate beneficial post-mining use.' So that House Bill 1717 said to, 'restore insofar as practical to appropriate beneficial use. I think that's too weak, whereas I think the House Bill 656 that would call you to restore it to at least the use it had prior to the mining may also be too tight the other way. I think the Senate Bill 55 approach is down the middle of the road which says that you do restore it to the 'same or substantially beneficial use,' is a proper way to go there." Therefore, the conclusion that we have drawn from the legislative history of the bill is that the extent of reclamation required by "substantially beneficial" may be something other than the use it was prior to

Jan 1, 1979

By M. F. Burr, F. V. Lenel, G. S. Ansell

The mechanism of materials transport was studied in a model experiment in which a silver sphere was sintered to a silver plate under an applied external stress near 800° C. For this purpose the rate of growth of the neck between the sphere and the plate which is proportional to the strain rate of the creep process involved in a neck growth was determined by measuring the change in electrical resistance of the away. This rate of neck growth will depend upon the magnitude of the applied external stress. By measuring the rate just before and just after a change in the external load and therefore the applied stress, the relationship between strain rate and stress can be derived. For material transport by slip in a pure metal it is expected that the strain rate should be proportional to the 4.5th power of the stress, while for transport by diffusional flow the strain rate should be proportional to the first power of the stress. It was found that for stresses above 5 X 10' dynes per sq cm (70 psi) the exponent in the stvain rate-stress relationship was near 4.5 while for a stress of 0.7 x 108 dynes per sq cm (10 psi) an exponent of 1.8 was determined indicating that under the conditions of the experiment the transport mechanism for creep in silver shifts from diffusional flow to slip in the region of 0.7 x 106 dynes per sq cm (10 psi). The importance of these findings for an understanding of the mechanism of material transport in conventional sintering (without an external load) is pointed out. In a paper by Early et al.,' the mechanism of material transport during sintering was treated as a creep process. It was pointed out that two possible types of creep processes could operate during sintering. In one of these material transport takes place by vacancy diffusion due to a gradient in chemical potential. The vacancy sinks in this diffusion process may be either grain boundaries, as in Herring-Nabarro microcreep, or regions beneath a surface of small radius of curvature. The diffusive transport may be by volume, grain boundary, or surface diffusion. In the other mechanism, creep takes place by slip, i.e., dislocation motion with its rate generally controlled by dislocation climb. One method of distinguishing between these two modes of materials transport is to investigate the creep rate, i.e., the rate of material transport as a function of stress. For material transport by vacancy diffusion, the creep rate is proportional to the stress.' For creep by slip, controlled by dislocation climb, the creep rate is proportional to a power of the stress. For pure metals this power is 4.5;374 for dispersion-strengthened material a fourth power relationship can be derived.5 This difference in the stress dependence of the strain rate is illustrated schematically in Fig. 1, in which the logarithm of strain rate is plotted vs the logarithm of the stress for material transport in a pure metal by vacancy flux and by dislocation climb. The stress range in which the two types of material transport overlap would be expected to be relatively small. In the experiments described by Early and coworkers compacts pressed from spherical copper powder were sintered isothermally under an applied axial external load in a dilatometer. During sintering the magnitude of the applied external load was changed and the rate of axial shrinkage of the compact before and after the load change determined. In order to find the stress dependence of the strain rate the magnitude of the stress acting on the neck area between the spherical particles before and after the load change had to be calculated. This stress is the resultant of the stresses due both to the externally applied load and to surface tension. The stress due to surface tension is a function of the geometry of the powder compacts. It can be determined, at least for simple geometrical arrays,'76 but it is difficult to obtain exact values of the stresses for actual powder compacts when only average values of particle diameters and of neck diameters between particles are available. The calculation of stress and the strain rate-stress relationship is therefore only very approximate.

Jan 1, 1968

By Fuad S. Maayeh, Robert J. Evans, Paul M. Yavorsky

A description and capabilities of the Mine Roof Simulator at the Pittsburgh Mining Technology Center is illustrated for testing longwall roof support equipment. This unique Mine Roof Simulator has the capacity to exert 3 million lbs. of compressive force vertically and 1.6 million lbs. of force horizontally to simulate loads on hydraulic supports typically found in longwall mining. The supports that undergo testing are instrumented with strain gauges and photoelastic coatings such that critically strained areas become readily apparent. These critically strained areas are redesigned or retrofitted with appropriate reinforcement and retested. A data base will be accumulated from several support designs that will lead to an optimized design that will have the potential to reduce downtime by malfunctions of supports and thus increase productivity. A typical test procedure and analysis is given for a two leg 350 ton shield along with a description for placement of strain gauges, displacement gauges, and hydraulic pressure monitors for critical sites.

Jan 1, 1982

By Oliver Bradley

THE utilization of casing-head gas in the manufacture of casing-head gasoline by both the absorption and the compression method is a most important factor in the conservation of our natural resources.. Any industry connected with the oil business, in general, possesses particular attraction for a large number of people not conversant with its basic principles, for the reason that the large fortunes made in the production and utilization of petroleum and its products have been given undue prominence. The general impression of the public that enormous profits are to be realized in the casing-head gas industry with minimum expenditures of both capital and effort has, in a large measure, accounted for the phenomenal expansion of the industry in recent years and, likewise, has resulted in many mistakes and loss of investment funds. It is true that many installations have been very profitable, but such instances are always the result of careful planning, experienced judgment and conservative estimates. The inception and subsequent activity in the manufacture of casing-head gasoline, enabling the business to assume an important position in the petroleum industry, are of, comparatively recent origin, as its greatest growth, particularly in Oklahoma, occurred during the years 1917 and 1918. Much information must yet be secured and systematized concerning the methods of manufacture of gascline from high-yield casing-head gas, and a large field is still open for the application of accumulated experience and good engineering practice in devising better methods of extracting gasoline from casing-head gas of the poorer grades. The absorption process is coming into general use as a most efficient system of treating casing-head gas, and even so-called dry gas. In fact, there is a decided tendency toward the universal adoption of the absorption process as against compression methods. However, a general discussion of the relative merits of these two systems is not within the scope of this article.

Jan 9, 1920

By Harold S. Morgan

INTRODUCTION The Waste Isolation Pilot Plant (WIPP) is being developed in southeastern New Mexico by the United States Department of Energy as a research and development (R&D) facility to demonstrate the safe disposal in salt of radioactive wastes resulting from defense activities. As part of the WIPP R&D program, a series of in situ tests will be performed to determine the behavior of drifts and storage rooms in the creeping salt medium (Matalucci, et al. 1982). Data obtained in these tests will be used to evaluate and improve numerical models used to compute the structural response of these drifts and rooms. Stress has been proposed as one of the parameters to be measured in the tests, and borehole inclusion stressmeters have been included in the instrumentation package. Cages of this type provide an indirect measurement of stress change in that they actually monitor borehole displacements which are then related to changes in the in situ stress away from the borehole. The relationship between stress and displacement is highly dependent upon the constitutive behavior of the rock in which the gage is emplaced. This relationship is well understood for rocks with linear stress-strain behavior (Fossum, et al, 1976), but, for creeping rocks like salt, the relationship has yet to be determined. Thus, inclusion gage response in salt must be investigated fully before stress measurements from the WIPP in situ tests can be used for comparisons with computed stresses The calculations presented in this paper were performed as part of an investigation of inclusion stressmeter performance in salt. They focus on the strain gaged stressmeter (SGS) (Cook and Ames, 1979) and on a hypothetical solid cylindrical inclusion with variable stiffness Issues addressed include the effects of creep and the effects of gage stiffness on stressmeter output for various loading conditions. The

Jan 1, 1984

Discussion of the paper of FRANCIS S. PEABODY, presented at the St. Louis meeting, October, 1917, and printed in Bulletin No. 125, May, 1917, pp. 775 to 781. THE CHAIRMAN (CARL SCHOLZ, Chicago, I11.).-Coal wastage is undoubtedly one of the most prominent topics before the coal operators of the United States today. Even those who have been in the business only 25 years, like myself, know that the exhaustion of coal is something that should and must, be curbed. If it is not, before long we shall discover that the great coal resources of the country are not what we-thought they were; we have been so accustomed to work at the best and thickest coal alone, that it will be difficult for us to realize one of these clays-and that (lay is not far distant-that we are no longer the rich nation in coal that we thought we. were. In this connection I feel obliged to attach a little blame to the Geological Survey for misleading the people. There are several members ,here who assisted in that work, and I am going to ask them to defend themselves. The Geological Survey deals with coal seams of much less thickness than we could now expect to, mine, particularly with the present high wages, excepting at a prohibitive cost. The Geological Survey, in its estimates, does not discriminate between thick and thin seams, but simply estimates our resources at so many hundred thousand billion tons of coal. I believe they include seams from 15 to 18 in thick, but you all know that a vein below 3.5 or 4 ft. is not considered economical to mine at this time. R. V. NORRIS, Wilkes-Barre, Pa.-Mr. Peabody has evidently been thinking almost entirely of Illinois conditions, with which I regret to say I am absolutely unfamiliar. In some West Virginia mines the total recovery at present is considerably over 90 per cent. and extraction-, as high as 97 or 98 per cent. are claimed.

Jan 1, 1918

By G. B. Misra

Though resistance to flow offered by mine airways supported with timber sets has been an object of study over the last half century, no accurate relation has yet been established from which prediction of the resistance coefficient of a projected timbered airway can be made. Zenofontowa et al. developed an empirical relation, but this relation has not been found to satisfactorily correlate experimental data obtained by Sales and Hinsley. This led the author to develop a set of simple theoretical relations between the resistance coefficient of timbered airways and the various parameters affecting it, such as the type and spacing of sets as well as the shape and size of members forming the set. Experiments were designed with the help of a laboratory model airway to verify the validity of the relations developed. With the experiments conducted so far with 4, 3 and 1-piece sets of 3.4 x 3.4, 2..5 x 2.5, and 4.5 X 4.5-cm square-section timbers in a 45.8 x 38-cm model airway, the theoretical relations have been shown to hold.

Jan 1, 1972

The following Nominating Committee having been already appointed and approved by the Executive Committee in accordance with authority vested in the Executive Committee by the Board of Directors, was approved by the Directors: John V. N. Dorr, Chairman, Percy G. Beckett, J. W. Hutchinson, Julian Kennedy, William H. Linney, Charles W. Merrill, and E. Gybbon Spilsbury. The question of the purchase of Liberty Bonds, as well as that of bringing to the attention of the members the advisability of the purchase of these bonds, was referred to the Finance Committee. Sixty Members, four Associates, and thirty-six Junior Members were elected. Two Members were reinstated. Eight resignations were accepted.

Jan 7, 1917

Correlation between Metallography and Mechanical Testing By H F MOORE (Henry Marion Howe Memorial Lecture Trans, vol 120 11,000 words ) The lack of effective correlation between metallography and mechanical testing from the days of Reaumur to the present is noted, and two general problems of such cor¬relation are stated (1) the correlation of qualitative test results with quantitative, and (2) the correlation of average results with maximum or minimum results Some correlation has been achieved, notably in the field of heat-treatment and in the study of elastic strength of metals Correlation is in the process of being developed in several other fields, including the quantitative study of the effect of grain size of metal on mechanical properties, of grain size and type of crystalline structure on the sensitivity of metals to weakening at holes, notches and other "stress raisers," and in the study of the starting phases of spreading, "fatigue" cracks Correlation of mechanical test results and metallographic study is needed in the study of such problems as the various theories of failure of metals, the meaning of and tests for service ductility of metals, and the relative damaging effect of defects inherent in metals, such as minute cracks and segregation, as compared with the damaging effect of "imposed" stress raisers, such as screw threads, sharp shoulders, etc The neces¬sity for more correlation of metallography and mechanical testing during student days is emphasized, and also the need of a better understanding on the part of engi¬neers of the significance and limitations of metallographic apparatus and results and of X-ray diffraction This should be matched by a better understanding on the part of metallurgists of the significance and limitations of mechanical tests of metals, of testing machines and strain-measuring apparatus

Jan 1, 1937

By M. W. Clegg

The application of the Laplace transformation to problems in the flow of compressible fluids in porous media has provided a large number of exact solutions. For plane radial flow, however, these solutions are either complex integrals or infinite series and are of little value to the field engineer. In the case of production at constant well pressure, the available approximate solutions me valid for large times only. In this paper it is shown that an approximate inversion formula for the Laplace transform, developed for the solution of viscoelastic problems, is applicable to radial flow problems and provides simple analytical solutions to constant terminal pressure problems. The method may be used to obtain approximate solutions to many problems, including media with radial permeability discontinuities, multi-layer formations and pressure buildup in wells after shut-in. The results are compared with the few available computer solutions as well as the large time solutions, and it is shown that this approximate method greatly extends the time interval over which a simple analytical solution is acceptable. INTRODUCTION The study of transient problems in the flow of fluids through porous media has benefited greatly from the application of transform methods. The use of the Laplace transformation for solving parabolic equations has been widely discussed in the field of heat conduction and diffusion as well as in the petroleum literature. Removal of the time variable with the Laplace transformation generally reduces the problem to a boundary value problem which may be solved by standard techniques. A much more formidable problem then faces the engineer, however, for frequently the transform does not possess a simple inverse. The result is that the general inversion integral must be used and this leads to either an infinite integral or an infinite series, both of which are difficult to handle from a computational standpoint. Asymptotic approximations for the inverse have been known for some time and these yield approximate inverse functions that are valid for very large or very small times — but frequently the times of interest lie somewhere between these two extremes. Therefore, some acceptable approximation valid over a larger interval of time is desirable. During the past few years a number of methods for achieving this have been developed and some of these are discussed briefly in this paper. The relative merits of the various methods are not evaluated here, but some general conclusions reached by other authors are given. One of these methods has been applied to problems associated with the radial flow of compressible liquids to producing wells. In the case of production at constant well pressure, the method leads to simple analytical solutions for a number of standard problems; e.g., homogeneous formation, permeability discontinuities, pressure buildup. These solutions greatly extend the range of validity of the asymptotic ones (valid for large times only) and should be of value in studying the behavior of wells producing under constant pressure conditions. METHOD FOR THE APPROXIMATE INVERSION OF LAPLACE TRANSFORMS Much of the work that has been done on the approximate inversion of Laplace transforms has originated in viscoelastic problems. Apart from the asymptotic approximations,1 one of the first approximate methods was due to Alfrey.2 If (s) is the Laplace transform of f(t) defined by

By John V. Beall

There was optimism on 14th Street on April 22, Earth Day. We only have the report second hand because the demonstration conflicted with another appointment. Fifth Avenue was closed to vehicular traffic from 14th Street to the Park for a few hours and the crowd that showed up to promenade rivaled anything that can be imagined, even one at a country fair in Merry Old England. Certainly the domestic animals were there and the costumes were wild-as they are almost any day on 5th Avenue. However, the mood was friendly, happy and optimistic according to one of our neighbors who filmed and taped interviews with some of the characters. People think the air is going to be clean, and the water pure in the future. Land is going to be treated with respect. Even if the demonstration temporarily fouled the streets with litter, it served the purpose of dramatizing awareness. In talking to our friend about his experiences we didn't miss the opportunity to sound out his impression of whether or not people recognize that no group of people nor industry has a monopoly on pollution.

Jan 1, 1970

By A. D. LeClaire

This paper claims to provide a description of diffusion processes in solids which is said to be a reformulation of Fick's Laws and therefore, presumably, is supposed to be as general as those laws. In fact, it appears to provide no more than an atomic model of a rather restricted type leading even to results in conflict with experiment. The restriction lies in the assumption, carried throughout the paper, that even in a chemical gradient the jump frequency i of an atom of species i is a function only of the composition on the plane from which it jumps, i.e., ?i = ?i(cl, c2 ...). This means that atom jumps in opposite directions from a site would occur with equal probability. There would then be no tendency for atoms to migrate preferentially in one direction along the gradient, so the model is incapable of accommodating the well established phenomenon of atom drift in a chemical gradient.10-" A more general model that does not suffer this difficulty was discussed in a paper13 I wrote in 1958, and the results therein already contain as a special case those given by Dr. DeHoff. The simplest sufficiently general assumption is to suppose that ?i is a function ?i(a1 a2,...; wl, w2, ..-) of the concentration aj and ? ?j at the site from which and to which, respectively, a jump is made. Any such function can always be expressed as a function of the sum and difference of its arguments. Thus d is the jump distance and g a geometrical constant. Obviously this is zero, i.e., no drift, if ??ri/??j = 0. X is written in this form, revealing two components of the total drift, because it can be shown that only the second component, depending on ??'i/???(?j -aj), actually contributes to the net diffusion flux Ji. This component can be shown,13 by a straightforward ther-modynamic transcription, to be responsible for the so called "thermodynamic factor" in the Darken approximation for a chemical diffusion coefficient is the activity coefficient of i. Because the jump rate ?i in DeHoff's approximation has no dependence on the concentration gradient it does not seem possible to derive the Darken equation from his Eq. [6] without the further rather arbitrary assumption that ?i = const ri. It is to be noted too that the author's derivation of Eq. [12] is only valid when ?i is in fact a function only of the cj at the plane from which the atom jumps—for only then is ci?i a unique function of position and therefore of A. Author's Reply R. T. DeHoff I am indebted to Dr. LeClaire for his penetrating discussion of my paper, "A Reformulation of Fick's First Law". I concede that it does appear initially that the relationship presented in my paper could be derived from the detail atomic model of random walk and atom drift presented in Dr. LeClaire's approach. However, there are some important differences in concept and viewpoint which deserve further amplification. Dr. LeClaire's description is penetrating, detailed, and fundamental. His approach describes an extremely complex phenomenon, the displacement of atoms in a multicomponent gradient, at a sophisticated level. For precisely these reasons, his analysis has not proved to be useful for experimental studies that have practical objectives. For example, in order to obtain the information required to complete the analysis of the jump frequency distribution in a ternary system, the following series of experiments would, I believe, be required: 1) chemical (gradient) experiments, covering the composition range;

Jan 1, 1970

The First Conference of the Powder Metallurgy Committee convened in the East Foyer of the Hotel Waldorf-Astoria, New York City, at 9:45 a.m., on Feb. 21, 1944, Mr. John Wulff, General Chairman, presiding. THE CHAIRMAN.-In behalf of the American Institute of Mining and Metallurgical Engineers I welcome all members and guests to this conference on Powder Metallurgy. We hope that this meeting will give expert and novice in the field a chance for discussion. Unfortunately, the subject has been overemphasized by some, and, of late, severely criticized by others. We have here today powder producers, fabricators, and engineers of different viewpoints, who can make the meeting a success. Such success depends not only on the caliber of the papers presented but more so on the discussion. To give you time for a free exchange of views, the papers have been shortened purposely. With the hope that you will all benefit by this conference, I shall turn the meeting over to the Chairmen of the morning session, Mr. Roland P. Koehring, of Moraine Products Division of General Motors, and Dr. R. K. Waring, of the New Jersey Zinc Company. SESSION ON DESIGN FACTORS IN POWDER METALLURGY R. P. Koehring and R. K. Waring presiding The opening paper of the session was presented by Mr. Fred P. Peters, as follows:

Jan 1, 1945

By J. T. Ryan

WITH J. T. Ryan, of Pittsburgh, in the chair, 40 men on Monday afternoon were attracted to the first meeting of the new Health and Safety in Mines Committee. The speakers were well received and the discussion was good and virile. The field and scope of the new Health and Safety in Mines Committee was reviewed briefly, yet concisely, by Scott Turner. This committee is to cover the whole mining industry, in which much progress in reducing accidents has been made in recent years. Members of the A.I.M.E. can considerably assist in this important problem.

Jan 1, 1933

By S. LeFevre

THE solution of the housing and sanitation problem in mining communities, keeping in view both economic and humanitarian aspects, demands the best thought of the management of such enterprises. Upon the solution depend the health and comfort of the employee and his family, and as a consequence his contentment and efficiency. The following description covers briefly the methods installed for Witherbee, Sherman & Co. The operation of the system has been for about two years under the direct supervision of T. A. Hammond, Land Agent, and I am indebted to him for a compilation of the results.

Jan 2, 1915