Search Documents

COUNCIL OF EDUCATION OF AIME (Formerly Mineral Industry Education Division) Established as a Division January 15, 1932 Established as a Council February 26, 1957 John C Calhoun, Jr, Chairman 0 Cutler Shepard, Vice-Chairman Thomas A Read, Secretary-Treasurer Dept of Mining & Metallurgical Engrg University of Illinois Urbana, Illinois COUNCIL OF ECONOMICS OF AIME (Formerly Mineral Economics Division) Established as a Division December 15, 1948 Established as a Council February 26, 1957 Louis C Raymond, Chairman Lorin A Cranson, Vice-Chairman Henry T Mudd, Vice-Chairman Adam K Stricker, Jr, Vice-Chairman Paul F Yopes, Secretary-Treasurer U S Bureau of Mines Albany, Oregon

Jan 1, 1957

By E. C. Wright

FOR many years the cost of making pig iron and steel in the Birmingham district has been about the lowest in the United States. The close proximity of the important raw materials such as coal, iron ore, limestone, and the large available scrap supply made it possible to assemble all of the important ingredients necessary for steel- making with only nominal costs for transportation. Both iron ore and coal were being mined in this district at one time for about $1 per ton from underground operations. At that time mining wages were low everywhere and the labor rate in the South was considerably below that of other mining districts. This situation persisted until the emergence of labor unions as an economic and political force, emigation of southern labor to northern plants, and continued growth of industry in the South in the years following the depression of 1932. Since that time union organizing of miners and steel workers throughout the nation has increased labor costs in mining and steelmaking. This influence has been felt particularly in underground mining operations since the proportion of labor cost to total cost is still high. The previous advantage in basic labor rate in the South has been almost entirely eliminated by the equalization of labor rates in basic industries by national unions. Since 1945 these influences have been especially noticeable in increasing the cost of mining coal and iron ore in the South. The northern steel districts are still being largely supplied with iron ore from the Minnesota open-pit mines and the cost of this ore has not increased nearly as much as the cost of ore obtained from underground mines in Birmingham. A similar situation exists in coal mining; the thinner seams in Alabama are not so amenable to mechanization as the northern mines and, as a result, the output per man-day in southern mines is only about three tons of coal as compared to five or six tons per man-day in the large captive mines of West Vir-

Jan 1, 1950

By Richard L. Gordon

THE PROBLEMS AND POSSIBLE SOLUTIONS Toward the end of the 19th century, American industry began a drastic reorganization. The many, small, often-regional firms were supplanted by large national corporations-often produced by mergers among the existing firms. Giant companies appeared throughout American industry and many of them were engaged in the mineral industries.a The largest combines, by far, to emerge during the period were United States Steel and Standard Oil. Long before the restructuring had run its course, widespread concern arose over the process of concentration. Efforts were made to control, if not stop, the transformation. The concern produced the Sherman Antitrust Act of 1890 and the first of many federal regulatory agencies-the Interstate Commerce Commission (see Refs. 24, 31, 42). The basic objectives of these policies remain unclear to this day. The crucial issue is whether the goal is primarily to insure development of a more competitive economy or to preserve a social structure leaving more scope for small businesses. Complications arise from difficulties in agreeing upon the meaning of these terms. Studies of the early years of the antitrust movement suggest that it involved no particular concern over the mineral industries. Objections were directed at big companies in general. To be sure, the conservation movement arose in roughly the same period and did stress the evils of monopoly control of minerals. However, direct, continuing influence of conservation policy on antitrust is not apparent. Many of the most important antitrust cases, nevertheless, involved minerals. This, of course, may be sheer coincidence; the choice of cases has never followed any obvious pattern. Certainly, no simple hypothesis can explain the interest consistently. Once it may have been true that mineral industries were more likely than other sectors to be dominated by a few large companies. Yet, often sharp reversals of such tendencies -e.g., in oil and aluminum-have not removed antitrust interest. The importance of minerals to the economy cannot satisfactorily rationalize antitrust interest. The equally

Jan 1, 1976

By T. A. Rickard

The history of this State is that of one generation. Thirtysix years only have elapsed since the birth of that beneficent industry whose footsteps were the first to traverse the wilderness of the prairies and penetrate the solitude of the mountains. So soon is history made. The men who halted on the rolling plain where Denver now stands and gazed westward at the snow-clad ranges in eager questioning of their possibilities of golden wealth, have lived to see a noble city built where once their camp-fires burned, and have participated in the discovery of a magnificent series of productive mines amid the mountains which seemed at that time the Ultima Thule of their pilgrimage. To those who investigate the workings of our complicated mining and metallurgical industries, the story of their evolution from humble beginnings will appear an instructive romance. The record that tells it presents features common to the growth of modern mining regions, but also bears aspects peculiar to

Jan 1, 1897

By W. A. Clark, E. H. Dresser

ORE from the Minnesota iron ranges is transported from the mines to the loading docks on Lake Superior over four different railways: the Great Northern, Northern Pacific, Soo Line, and Duluth, Missabe and Iron Range, with hauls varying from 60 to 110 miles. For this service a large amount of specialized equipment is used. The steel ore cars are of the hopper type, 24 ft. long, to dump into alternate pockets of the docks, these pockets being 12 ft. long to correspond with the 12 or 24-ft. spacing of the boat hatches. The more recently con-

Jan 1, 1941

By G. H. Wigton

The oxidized ores of the Chief Consolidated Mining Co., in the Tintic mining district, have never yielded to metallurgical treatment by any standard method except smelting. These ores occur in comparatively small, irregular, siliceous replacements in limestone, and carry silver, lead, and gold as the principal valuable metals. But smelting methods are unsatisfactory, as the lead smelters heavily penalize the largc amount of silica in the ore, and the copper smelters do not pay for the lead in the ore; therefore, an alternative treatment method was sought. In 1916, a metallurgical research department was organized under the direction of the writer. Many standard metallurgical methods were investigated but, on oxidized ore, none yielded extraction great enough to make its use feasible. During some chloridizing-roasting experiments in 1916, made in an assay muffle, the writer noted that large proportions of the silver, lead, and gold were volatilized from certain oxidized ores. The possibility of volatilizing the metals and collecting them in the form of a concentrated fume was then studied. But, as it was shown that satisfactory chloride-volatilization would be limited to a furnace feed with a high fusing temperature of the non-volatilizable constituents, and as the results obtained in a rotary kiln with the admixture of common salt with the ground ore were inferior to muffle tests, further volatilization experiments were discontinued until 1920. During this internal, an expcrimental sulfidizing and flotation plant was operated. After the cessation of attempts to float the oxidized minerals, chloride-volatilization experiments .were resumed. The highly infusible flotation tailing from the operation of the flotation mill was used for furnace feed. The first tests made on flotation tailing mixed with 10 per cent, common salt showed nearly complete lead and gold volatilization but considerably less volatilization of silver than in muffle tests. In attempts to increase the silver extraction, the percentage salt in the furnace feed was varied, and it soon became apparent that the use of smaller percentages of salt raised the fusion temperature of the furnace charge and thus

Jan 1, 1926

By Richards J. W.

J.W. RICHARDS, South Bethlehem, Pa. (communication to the Secretary?).-Mr. Howland's paper, data and conclusions have interested me intensely, and have led me to study carefully the record-of his 26 furnaces therein given. Mr. Howland is undoubtedly right in his conclusion that when expressing the amount of carbon burned at the tuyères in percentage of the total

Jan 1, 1917

F. E. BASH, Philadelphia, Pa.-In order to make a definite check on the emissivity of crucible steel under works conditions, a test was planned and executed by the plant of the Midvale Steel Co., by a Sub-committee, as follows: Five crucibles were put in a crucible furnace with-the normal charge and were treated in the same manner as a number of others that were charged at the same time; the only difference was that the five cur-cibles had lids with.2-in. holes in the center. It was thought that after the crucibles were removed from the furnace a reading could be made through the hole in the lid with the optical pyrometer and that such a reading would give the true temperature of the steel as black-body con-ditions should prevail inside the crucible. If after obtaining the true temperature, the crucible lid were removed and the steel poured into the ladle, the apparent temperature could be taken by sighting on the steel stream and the emissivity obtained from the two temperature values. Such a test was carried out with five crucibles. About a third of the crucibles charged into the furnace with the five experimental ones were first drawn from the furnace and poured into the ladle. The experimental crucibles were then drawn and readings of the true temperature were made

Jan 12, 1919

By A. Becker, J. A. Slankis

Equipment has been developed to utilize natural 8 Hz electromagnetic fields to measure rock resistivities. Telluric and magnetotelluric surveys have detected resistivity variations associated with geological contacts and metallic sulfide deposits. The fundamenfa1 premises of these methods are illustrated by the results of surveys across a Pleistocene-Precambrian contact in the Ottawa Valley and a near-surface sulfide deposit in Northern Quebec. Such interfaces are characterized not only by variations in apparent resistivity, but also, unexpectedly by the spatial anisotropy of the electric fields and the presence of a strong vertical magnetic field component in their vicinity. Standard geophysical electrical and electromagnetic methods (Heiland, 1940) for the determination of the electrical properties of the ground and the search of good electrical conductors necessitate the use of a transmitter and receiver which are coupled galvanically or inductively through the ground. The electrical properties of the ground are deduced from either the transfer function, or the impulse response, of the transmitter — ground — receiver system. Where deep penetration is desired these methods require powerful transmitters whose weight and size increase the cost and reduce the speed of operation. It is possible however, to resort to another class of electrical prospecting methods which employ ambient, natural electromagnetic fields in place of a transmitter.'-' In the audio and subaudio frequency ranges, these fields are generated by thunderstorm activity. At some distance from the seat of the disturbance, the e.m. fields propagate as plane waves with a horizontal magnetic field component. The incident wave, of course, induces currents in the ground. Where the ground is homogeneous the relation between the horizontal magnetic and horizontal electric fields vectors is particularly simple:' /E/ = \[SpT/H/ (1) where: /E/ = magnitude of horizontal electric field in millivolts/kilometer (RMS) /H/ = magnitude of the orthogonal inducing magnetic field in milligammas (RMS) p = rock resistivity in ohm-meters i = frequency of measurement in c/s In practice, the ground is seldom an homogeneous half space, lateral conductivity variations exist, (in the case of base metal prospecting these are the features actually sought) and the two field vectors are no longer simply related. The ratio of E to H is still useful, however, for the determination of an "apparent" ground resistivity. From a theoretical view point, the general problem of a two dimensional fault or dyke anomaly can be separated into two distinct cases. In the first case, where the e.m. energy propagates in a direction normal to the strike, the horizontal magnetic field remains constant and is oriented along the strike of the formation.3 As shown by d'Erceville and Kunetz," all the information about the anomaly is contained in measurements of the electric field component. In fact, away from the interface, the electric fields are proportional to the square roots of the resistivities:

Jan 1, 1970

By J. B. Newsorn

VERTICAL SHAFTS in the United States have heretofore been sunk by blasting and mucking. The blasting leaves uneven, shattered walls which usually must be supported. Even though the walls will stand, shaft lining is needed to furnish supports for the cage guides, pipes, and power conduits. The lining is generally timber, and as timber can be most easily framed into rectangles, rectangular shaft openings are the rule. The timber reduces the size of the cage floor. For example, if the Idaho Maryland company had put down No. 2 shaft by blasting and mucking, the cage area would have been about thirty per cent of the total shaft area. Besides a low percentage of useful area, an ordinary shaft is subject to fire hazard and to timber maintenance charges. It is also poor for ventilation because the timber ribs cause eddies which greatly reduce the speed of the air currents. A bored shaft does not have these disadvantages. The walls are smooth, circular, and not shattered by blasting, so lining is not required in most

Jan 1, 1936

By William Kelly

I AM-glad to have the opportunity at this time to say that I consider it a very great honor to be elected President of the American Institute of Mining and Metallurgical Engineers. It fulfills the proudest hopes of my ambition. There is, ,however, one drawback to my personal gratification-a feeling of unworthiness to have my name placed on the list with former Presidents of the Institute, with the brilliant Raymond who guided our society for so many years, with the versatile and lovable James Douglas, my first employer and my friend, a most generous benefactor of our Institute, with the skilful Holley, who gave to the manufacture of steel in this country, its first great impulse, to mention only three of the accomplished men who have preceded me. I assume that the honor of my being elected President of the Institute is not merely a personal one but that it should be considered a tribute to the wonderful progress in the art of mining, both underground and in open pits, and in the beneficiation of native copper and iron ores, which have been shown in the Lake Superior District and also a recognition of our members there and elsewhere who are living at the mines and directing the operations, upon the success of which the whole mineral industry depends.

Jan 1, 1924

By AIME AIME

LOCAL COMMITTEES. GENERAL RECEPTION COMMITTEE.-Mr. and Mrs. H. S. Chamberlain, Mr. and Mrs. J. T. Lupton, Mr. and Mrs. T. H Lasley, Mr. and Mrs. R. S. Faxon, Mr. and Mrs. H. Clay Evans, Mr. and Mrs. C. E. James, Mr. and Mrs. B. F. Thomas, Air. and Mrs. H. S. Probasco, Mr. and Mrs. W. M. Lasley, Mr. and Mrs. L. W. Llewellyn, Mr. and Airs. T. G. Montague, Mr. and Mrs. E. B. Thomasson, Mr. and Mrs. C. F. Milburn, Mr. and Mrs. C. A. Raht, Mr. and Mrs. C. C. Notting¬ham, Mr. and Airs. Z. C. Patten, Mr. and Mrs. Willard Warner, Mr. and Mrs. S. R. Read, Mr. and Mrs. Carl White, Mr. and Mrs. M. M. Allison, Air. and Mrs. C. E. Buck, Mr. and Airs. H. F. Temple, Air. and Mrs. M. M. Hedges, Mr. and Airs. X. Wheeler, Mr. and Airs. John A. Patten, Air. and Airs. N. T. Montague, Mr. and Mrs. R. H. Williams, Mr. and Mrs. T. R. Preston, Mr. and Airs. Morrow Chamberlain, Mr. and Airs. T. C. Thompson, Mr. and Airs. T. L. Montague, Mr. and Mrs. O. L. Hurlbut, Air. and Mrs. C. A. Lyerly, Mr. and Mrs. Garnett Andrews, Air. and Mrs. M. B. Ochs, Mr. and Airs. Webster James, Mr. and Mrs. D. P. Montague, Mr. and Mrs. Z. C. Patten, Jr., Mr. and Mrs. W. A. Sadd, Mr. and Mrs. J. B. Pound, Air. and Mrs. George D. Lancaster, Air. and Airs. J. F. Johnston, Mr. and Mrs. R. W. Barr, Air. acrd Mrs. W. B. Davis, Mr. and Airs. Douglas Baxter, Air. and Mrs. W. R. Crabtree, Mr. and Mrs. Lewis M. Coleman, Mr. and Mrs. Newell Sanders, Mr. and Mrs. E. Y. Chapin, Mr. and Mrs. W: B. Riddell,. Mr. and Mrs. J. B. Frazier, Mr. and Mrs. John A. Moon, Mr. and Mrs. C. D. Mitchell, Dr. and Airs. J. H. Race, Mr. and Airs. A. W. Chambliss, Mr. and Mrs. J. P. Smartt, Mr. and Mrs. J. F. Tarwater, Mr. and Mrs. L. D. Drewry, Capt. and Mrs. A. B. Putnam, Mrs. Minnie C. Ewing, Mr. G. F. Meehan, Mr. Sam S. Gerstle, Mr. P. A. Brawner, Mr. C. M. Preston, Air. George M. Guild, Mr. L. M. Mansfield, Dr. J. W. Johnson, Dr. J. AI. Hogshead. EXECUTIVE COMMITTEE.-H. S. Chamberlain, Chairman; H. S. Probasco, C. M. Preston, H. Clay Evans, J. T. Lupton, M. B. Ochs, C. C. Nottingham, Al. Al. Alli¬son, R. S. Faxon, C. E. James, C. A. Raht. EXCURSION TO CHICKAMAUGA PARK.-T. C. Thompson, Chairman; B. F. Thomas, G. F. Meehan, Morrow Chamberlain, W. J. Bass, J. K. McGoodwin. EXCURSION TO HALES BAR LOCK AND DAM.-R. H. Williams, Chairman; John A. Patten, Newell Sanders, George M. Guild, Capt. A. B. Putnam. EXCURSION TO ROCK-WOOD.-F. H. Clymer, Chairman; T. L. Brown, T. A. Wright, J. P. Tarwater, T. L. Peterman. INSTITUTE HEADQUARTERS.-The Hotel Patten. THE first session, held Thursday evening, Oct. 1, in the Banquet Hall of the Hotel Patten, was called to order by Capt. H. S. Chamberlain, Chairman of the Local Committee, who, in behalf of the city of Chattanooga, extended a hearty welcome to the members and guests of the Institute.

Nov 1, 1908

By J. W. Cunningham, M. J. Stultzman

THE demand for improved materials for high-temperature service has increased during the last few years. Iron,- nickel,- and cobalt-base alloys have been investigated extensively and many alloys with outs'tanding high-temperature strength have been developed. Considerable research has been directed toward improved methods of processing these alloys. The vacuum furnace as a tool for the purification and improved control of high-temperature alloys has been studied extensively and production units are in operation. The research covered by this paper studied the effects of casting in air, vacuum, or argon upon the elevated-temperature properties of two nickel- and two cobalt-base alloys. The alloys investigated were Stellite 31, He 1049, Udimet 500, and Guy Alloy. MELTING AND CASTING PROCEDURES Two heats of each of the four alloys under investigation were melted and investment cast under the following conditions: 1) Stellite 31 was melted and investment cast in air and in vacuum, with an argon atmosphere for pouring. 2) He 1049 was melted and investment cast in air and in vacuum, with an argon atmosphere for pouring. 3) Udimet 500 was melted and investment cast in vacuum with and without additions of zirconium and boron. 4) Guy Alloy was melted and investment cast in vacuum and in argon. The heats were all melted in induction furnaces equipped with preformed magnesia crucibles of 50-lb capacity. The air-melting furnace was powered by a spark-gap converter of 40 kw capacity. The vacuum-melting furnace was powered by a motor-generator set of 100 kw capacity. The argon heat of Guy alloy was melted in the vacuum melting furnace under an argon atmosphere. Virgin materials were used for preparing all heats except the air heats of Stellite 31 and He 1049. The charge for the air heat of Stellite 31 was a commercial blend of shot. The charge for the air heat of He 1049 was Stellite 6 shot plus those virgin materials necessary to give the desired composition. All of the materials used were of the same grade used com-

Jan 1, 1960

By AIME AIME

IN many countries the lack of liquid petroleum supplies has centered interest upon the hydrogenation of coal and coal tars for the preparation of motor fuel. In the United States, hydrogenation has been of greater interest for grading up low-value petroleum fractions to the more valuable volatile fuels and for the preparation of a variety of premium products, including aviation gasolines, solvents, Diesel fuels, and lubricating oils. Chemically, the basic reason for this process is that, as shown in Table 1, the ratio of hydrogen to carbon (H/C ratio) in available raw materials is quite different from that characterizing the products sought.

Jan 1, 1936

By C. W. MacGregor

In the testing of materials there exist various methods of recording graphically the behavior of a material subjected to tensile stress. Probably the most common method is to plot the tensile stress So, obtained by dividing the load P by the original area of cross section A0 at the start of the test, as a function of the strain e0, which is obtained by dividing the ?Lo or the change in the gauge length by the original gauge length Lo. A list of the symbols used here is given in Table 1. This method, while it has proved useful in the routine testing and comparison of various materials, does not have a very sound physical basis, as was first pointed out by P. Ludwikl, and consequently does not afford a very deep insight into the true physical behavior of the material under stress. Among the objections to this method may be mentioned: (1) that by dividing the load P at any stage of the test by the original area A. a fictitious stress is obtained, which does not actually exist; (2) that the strain e0 = ?L0 is not an exact expression for the true strain for large values of ?LO in per cent of Lo; (3) that when necking starts the strain varies considerably along the gauge length and the above expression no longer gives the true strain existing at any point on the outside of the bar; and (4) that the axial strain varies over the cross section of the necked portion and e0 does not represent an average of these strains over the cross section. Stresses taken from such a diagram would be only approximate and, if used to compare results of a test on a given material under simple tension with results obtained under combined stresses, certain errors would be thus introduced. In order to overcome some of these objections, various methods have been suggested, both as to the quantities to be measured and as to their graphical representation. In some cases the so-called "true stress," obtained by dividing the load P by the actual area of cross section A existing when the load P was applied, is plotted as a function of the strain

Jan 1, 1937

By HAROLD E. WHITE

LONG before the Stone Age, when man first sought shelter where there-were no natural shelters, such as caves and clefts in the rock, he uprooted trees and planted them upside down so that the roots formed the roof. By selecting trees whose roots grew out in a horizontal direction and; by planting these trees close enough - together, a crude shelter was formed. He then took mud, formed a plaster and covered over the' roots. Later the walls were made by using sticks and twigs and plastering between them. It is natural then, that he wiped his muddy hands on- his own hairy body and soon found that the mud was difficult to remove when, dry. It is due, to this discovery that we mix animal hair in 'our modern plaster to increase its strength. The use of fibrous asbestos in some refractory cements has followed this same principle.

Jan 1, 1929

By Bernard S. Borie

THE U-A1 binary system has been studied by Kaufmann and Gordon.' They have shown that three intermetallic compounds occur in the system: UAl², UAl², and a third compound tentatively identified as UA15. UA1³ is simple cubic, a, = 4.26A. Its unit cell contains one formula weight, and it is iso-morphous with AuCu³. UA1² is face-centered cubic, a, = 7.72A, with eight formula weights per unit cell. Rundle and Wilson have shown that it is iso-morphous with Cu²Mg.² A Debye-Scherrer pattern of the Al-rich compound indicated a more complex structure than either UA1² or UA1³. The following is a report of an investigation of the crystal structure of this compound and a determination of its stoi-chiometric formula. A melt of uranium (99.9 pct pure) and aluminum (99.9 pct pure) was prepared which contained about 25 pct U by weight. It was cooled from 950" to 650°C at a rate of 500" per hr and then taken from the furnace and air cooled. An X-ray diffraction pattern of the ingot showed only lines of aluminum and the Al-rich compound. Filings from the ingot were reacted with a solution of sodium hydroxide, producing a fine black powder, the diffraction pattern of which showed no traces of aluminum. A comparison of the Debye-Scherrer pattern of our sample with the data published by Kaufmann and Gordon1 showed that it is identical with the Al-rich phase which they reported. Single crystals were obtained by cooling the melt more slowly (about 50°C per hr). After reaction with sodium hydroxide, the crystals appeared as small black needles attached to the ingot surface. Cell Size, Space Group, and Uranium Positions A series of Weissenberg photographs for rotation about two of the crystallographic axes, taken with copper radiation filtered through nickel foil, revealed an orthorhombic cell of dimensions: a = 4.41 ± 0.02A b = 6.27 ± 0.02A c = 13.71 ± 0.03A Reflections of the type hkl were observed only if: h + k + I = 2n, of the type hkO only if: h = 2n and k = 2n, of the type h01 only if: h + 1 = 2n, and of the type Okl only if: k + 1=2n. Hence, the cell is body-centered with an 001 glide plane. The evidence for the existence of the glide plane is the observed extinction of 23 possible re- flections of the type hkO with at least one index odd. There are only two space groups consistent with these data: C"" — I2ma and D28 2h — Imma.³ he possible sets of atomic positions for these space groups are: 12ma: (0 0 0; ½ ½ ½) + 4: (a) x 0 %; x % % (b) x ¼ z; x ¾ Z 8: (c) x y z; x y z; x, ½ + y, Z x, M - y, z Imma: (0 0 0; ½ ½ ½) + 4: (a) 0 0 0; 0 ½ 0 (b) 0 0 ½; 0 ½ ½ (c) ¼ ¼ ¼; ¾ ¼ ¼ (d) ¼ ¾ ¾ ; ¾ ¾ % (e) 0 ¾ Z; 0 ¾ z 8: (f) x 0 0; x 0 0; x 1/2 0; x ½ 0 (g) ¼ Y ¼; ¾ Y ¾; ¾ y ¼; 1 y ¼ (h) 0 y z; 0; ;; 0, ½ + y, z; 0, l/2 - Y, Z (i) x 1/4 z; x ¾ z; ¼ z; x ¾ z 16: (j) xy z; x y z; x y z; x y z; x, ½ + y, Z; x,½ - y, z; x, ½ - y, z; 11 1, + y,Z Though density measurements on different samples were found to vary somewhat, they were all within the range 5.7 * 0.3 g per cu cm. If it is assumed that the unit cell contains four formula weights of UAl,, it is 6.5 g per cu cm. If there were as many as eight uranium atoms per unit cell, the

Jan 1, 1952

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 T. S. Lundy, R. E. Pawel

Effects of short-circuiting paths on observed diffusion behavior in real crystalline systems are considered. It is concluded that experimentally measured diffusion coefficients may vary widely from values associated with true lattice diffusion to those appropriate for short-circuiting paths alone depending upon the conditions of the experiment and the sensitivity and completeness of the data. IN 1961 Harrison1 classified experimentally observed diffusion behavior in systems involving both lattice and dislocation-enhanced atomic transport into three categories. His types A and C were limiting cases where the measured diffusion coefficients using the usual serial sectioning techniques were representative of lattice diffusion (with only slight effects of dislocations) and dislocation-network diffusion (with only slight effects from lattice diffusion), respectively. In both cases A and C for a sectioning experiment in which the diffusion couple has the semi-infinite geometry and unidirectional diffusion takes place from a plane source located at the origin of the coordinate system, he pointed out that Gaussian penetration behavior should be observed. For case A the lattice coefficient should be slightly enhanced by dislocation contributions, and the model of Hart2 can be used to predict the amount of this enhancement. For case C the observed coefficient should be that for the dislocation network and have little or nothing to do with lattice diffusion. Hart's model in its general form is still applicable, but the apparent diffusion coefficient for this case is virtually independent of dislocation density. Harrison's case B is that for which non-negligible contributions exist for transport by both mechanisms and "the concentration distribution does not approximate to any simple form." With the possible exception of very low temperatures where diffusion distances approach atomic dimensions, any real diffusion specimen will in general show non-Gaussian behavior provided the data are complete enough to uncover it. Thus, a "complete" set of data for any real system cannot be expected to be totally amenable to treatment by a simple mathematical model which does not take into account the relative distribution of transport by the various modes or submodes. For a particular sensitivity of specimen analysis and at a given temperature of annealing if the concentration profile could be observed as a function of time, "the behavior will initially be type C, and will develop into type B. and ultimately type A".1 Thus, it appears that the type of diffusion behavior which is experimentally observed in a given system depends very much upon the particular experimental conditions and the particular tools available to obtain the data. Interpreted in this fashion, Harrison's classification refers not to the diffusion behavior as a whole but to the relative sensitivity of the method of examination and completeness of the data. In the present paper we will: 1) assume that the measured penetration behavior follows the same general classification as that proposed by Harrison; 2) give, for diffusion in tungsten, examples of the range of diffusion coefficients that it is possible to obtain in a single experiment; and 3) speculate that some arguments which consider the possibility of short-circuiting effects being responsible for "anomalous" diffusion in several bcc metals may have been discarded prematurely.3 Both monocrystalline and polycrystalline tungsten were used in this work. The former was obtained as triple-pass, electron-beam zone-refined 6.0-mm-diam rod from Materials Research Corp.. Orange-burg. N.Y. The latter was swaged, high-purity bar stock which was annealed for 2 hr at 2200°C and 10-9 torr to yield an average grain diameter of about 25 /i. The tracer Nb95 was received in oxalate solution from the Isotopes Division, Oak Ridge National Laboratory. Experimental procedures of specimen preparation, isothermal diffusion annealing, serial sectioning by anodizing-and-stripping, and y counting of the individual sections to determine the tracer penetration profile after a given diffusion anneal have been described elsewhere.4 However, it should be noted that the anodizing-stripping sectioning technique has the particular advantage for this research of permitting sectioning to be accomplished over a wide range of

Jan 1, 1970

By AIME AIME

CHARACTERIZING the annual meeting as the biggest and best one yet has happened so repeatedly that some may suspect it has become a conventional phrase, like "good morning," and yet, what else can be said when not only one but all the many who express an, opinion use exactly those words, while the first of the two adjectives refers to a physical fact that is established by count. Perhaps there were hose who thought it not the best, but if so they were too tactful to say it out loud. So without further ado . let us admit that the one hundred and thirty-ninth general meeting of the A. I. M. E. held; as our By-laws provide, in New York during the third week of February, was the biggest and best of them all. Perhaps it is because we appreciate friendliness more as we grow older, but somehow the friendly atmosphere seems to rise slowly in temperature with the passing of the years. The actual atmosphere on the opening morning was quite the contrary, Feb. 17 being the coldest clay, so far, of this winter, and the suburbanites claimed that their thermometers had registered 5" below zero when they got up, though the official records of the weather man did not go that low. From that time the temperature steadily rose until Thursday afternoon, when the official record of 66" constituted a record high for Feb. 20 at New York. The weather man explained it by learned discussion of highs and lows, but we suspect the A.I. M. E. members must have had something to do with it.

Jan 1, 1930