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By Ira N. Holli

A meeting of Engineering Council was held on Thursday, Jan. 22, 1918, at the Engineering Societies Building, New York. Present: Chairman Ira N. Hollis (A. S. M. E.); Dr. Charles Warren Hunt, Alex. C. Humphreys and F. H. Newell (A. S. C. E.); B. B. Lawrence and .J. Parke Charming (A. I. M. E.); Charles Whiting Baker, D. S. Jacobus, and George, J. Foran (A. S. M. E.) ; H. W. Buck, E. W. Rice, Jr., N. A. Carle, C. E. Skinner and Comfort A. Adams (A. I. E. E.) ; Clemens Herschel and Calvert Townley (United Engineering Society); also, by invitation, D. W. Brunton, Chairman, War Committee of Technical Societies of Engineering Council. Of the several actions taken at this meeting, the following are selected as being of most general interest. Chairman-Baker-presented a resolution on the conduct of the war, to which objections were made. It was referred to a special-committee; Charles Whiting Baker, Charles Warren Hunt, and Calvert Townley, for re-drafting and presentation later in the meeting. The revised resolution submitted by this committee led to further discussion and as no agreement could he reached, the matter was laid on the table.

Jan 3, 1918

By C. C. Griggs

FROM its inception, a limestone quarry or mine should be under the direction of a capable engineer. Before it becomes a reality, he should outline the future results, plan the most economical methods for moving the materials and the most efficient equipment, and pilot the undertaking along the narrow pathway of success, avoiding the pitfalls of uneconomical production and the precipitous walls of scanty profits. Inspection of successful limestone properties shows that all have had difficult engineering problems, the solution of which have required keen engineering ability. In approaching a subject of this nature, it is logical to follow the progress of the limestone operation from its inception to the end, as reflecting the engineering required. There are four major divisions: Investigation, equipment, development, and operation.

Jan 2, 1925

By E. P. Mathewson

THE OLD Pueblo smelter is being dismantled after 43 years of continuous operation, from 1878 to 1921. It was built by Mather and Geist, on a bluff overlooking the Arkansas River just below the, city of Pueblo. At the time of its construction Pueblo was considered a most favorably situated town for a custom smelter. Coal, coke, fuel, limestone, iron ore, lead, silver, and, gold ores were plentiful. It was a "downhill pull" from all directions to Pueblo. Labor, both common and skilled, was plentiful and efficient. Leadville was in bonanza and there were not sufficient furnaces in Colorado to handle the ore offered. The plant prospered from the start. It soon required more capital; so the owners; with the assistance of Thomas Nickerson of Boston, at that time prominent in the affairs of the A., T. & S. F. railway, formed the Pueblo Smelting & Refining Co. About this time, also, very heavy shipments of rich silver ore from New Mexico began to come in. Agencies were established for the purchase of ores in the most important mining camps in the country from Kingman, Ariz., to Butte, Mont. Highly siliceous silver-bearing ores from Butte were shipped to Pueblo in train loads. This was used chiefly in the concentration of leady mattes. RECOLLECTIONS OF MR. GEIST, FOUNDER OF PLANT Mr. Geist is living in Guadalajara and has sent the following brief letter: "Early in 1878 the firm of Mather & Geist, which had been operating in Utah and had then closed their smelter there, after diligent search for a new location selected Pueblo. We erected the first smelter in the valley, blowing in the first furnace in 1878. Mather & Geist carried on until January, 1882, when they transferred all their business to the Pueblo Smelting & Refining Co., which had been organized in December, 1881. Full details of this transfer are given in the enclosed Report, which was issued early in 1882, for the purpose of interesting more capital, in which we succeeded admirably. "I personally did all the work of manager and super-intendent, some job in these days. My technical quali-fications were that I was a member of the class of 1866, Yale Sheffield Scientific. I was born in 1848, so was the youngest member of the class.

Jan 11, 1923

By G. B. Clark

Dynamic rock mechanic as it pertains to blasting has involved several areas of active research effort. Among the important problems which have been the subject of research are wave mechanics in rocks, mechanisms of rock breakage, cratering, applications of similitude, energy partitioning of explosives, coupling, and other related factors. In some of these areas many problems have received fairly complete answers, while in others, investigations have raised new questions while attempting to answer existing ones. The slabbing mechanism explains many of the phenomena observed in blasting, but is hot the complete answer to observed breakage and fragmentation phenomena. There is currently a gap between coupling experimental results and theory. Applications of similitude to open pit blasting have been made unnecessarily complicated. Basic scaling laws for large true and apparent craters have not been derived for either chemical or nuclear explosives. There are few useful data and little developed theory on the partitioning of energy of explosives in all types of blasting. No suitable mathematical model has been developed which will describe the stress waves in rock which are responsible for rock breakage: Significant progress has been and is being made in these areas of research, however. ELASTIC AND NONELASTIC WAVES Complete solutions for spherical wave equations in viscoelastic media are not available in the literature. Equations for certain viscoelastic models do show limited promise, however, of being applicable to rock masses, particularly for pulse type phenomena. Seismic investigations, blasting operations, the design of protective underground structures, and the evaluation of other explosive effects in solids would be greatly bene-

Jan 1, 1967

By Howard N. Eavenson

FROM the Pittsburgh coal bed in the four states of Pennsylvania, Ohio, Maryland and West Virginia has been produced an output that, at mine prices, represents a greater value than any other single mineral deposit in the world has yielded.12 While this distinction may in a few years pass to the gold reef of the Witwatersrand, it is possible that eventually, owing to the tremendous reserves still remaining, the ultimate yield of the Pittsburgh bed will be greater than that of any other known single deposit. Considering its importance, not a great deal has been written of its early history and development as a whole; most of the accounts have been of limited localities, or, at the most, of the area within a single state. In "Coal through the Ages" the writer mentioned some references to its early history, but this study will deal not only with its history but with the character of the bed, where and why it was first developed, and its effect upon the states in which it is found. It has not been the intention to write a detailed history of the development of the seam in each locality, as neither time nor inclination were available for doing such work, but only to show the influences that tended to hasten or retard such development. In general the historical matter ends about 1830, when geological surveys began to be made. Some of the maps show data available only since that time, and the sections about coal preparation and coking have been extended to the present time to show the changing conditions. It is believed that the early history includes all published records, and many more sources than those shown in the bibliography were consulted. It is quite likely that some references to coal in this area may be found in the unpublished papers of some of our early soldiers and colonizers, which exist in several libraries, and it is hoped that some future

Jan 1, 1938

By E. A. Steigerwald, G. L. Hanna

The influence of work-hardening exponent on the variation of fracture toughness with material thickness was studied for high-strength steel, aluminum, and titanium alloys. The results indicate that, when materials are compared at similar fracture toughness to yield strength ratios, the material with the lower work-hardening exponent undergoes the transition from flat to slant fracture at a larger thickness than material with a high work-hardening exponent. In the thickness range where complete slant fracture is obtained the reverse is true and a lower work-hardening exponent results in a lower fracture toughness. The influence of work-hardening exponent on fracture toughness is, therefore, dependent on the particular fracture mode. In the transition region a low work-hardening exponent is beneficial for fracture toughness while in the 100 pct slant region it is detrimental. THROUGH the use of fracture mechanics analyses, the influence of geometric variables on the crack propagation resistance of structures can be interpreted with reasonable consistency. However, in order to gain a more complete understanding of the fracture process, the influence of material parameters on crack propagation must be defined and coupled to the macroscopic fracture mechanics approach. The work-hardening exponent, which characterizes specific material behavior, may serve as an effective parameter to allow some degree of coupling to be accomplished. In the extension of a crack in a specimen of suitable dimensions the propagation process occurs in a stable manner when the crack extension force is balanced by the resistance to crack extension, which exists in the material at the crack tip. As the applied stress, and therefore the crack extension force, on the specimen increases, the resistance also increases primarily because the effective plastic zone at the crack tip, which is the main energy absorption process, becomes larger. Since the work-hardening rate of a material influences the stress-strain relationship, it will also influence the energy absorption process in the plastic enclave at the crack tip and hence should have an effect on crack propagation. A number of studies have been made correlating the strain-hardening exponent or the strain to tensile instability with the ability of a material to resist fracture. Gensamer1 concluded that a low-strain-hardening exponent would result in a steep strain gradient at the base of a notch. He reasoned that a large work-hardening coefficient would result in high-energy ab- sorption due to the increased area under the stress-strain curve. Larson and Nunes2 experimentally observed in Charpy tests on steels heat-treated to below 200,000 psi yield strength that the energy to failure in the fibrous mode, i.e., above the brittle-to-ductile transition temperature, was logarithmically related to the strain-hardening exponent. In order to avoid the complicating effects present in studying materials which undergo a brittle-to-ductile transition, Ripling evaluated the notch sensitivity of a variety of fcc metals with varying work-hardening exponents.3 The results indicated that the relative notch sensitivity, as determined from tests on specimens with a sharp notch, decreased with increasing values of strain hardening. Although the energy required for ductile or fibrous fracture increases with increasing work hardening, high-strength steels often exhibit improved crack propagation resistance when heat-treated to obtain low values of strain hardening.4,5 An analysis of whether low strain hardening is beneficial or detrimental to crack propagation resistance must depend on the particular fracture criterion involved. At temperatures where the material is relatively ductile and the development of a critical strain is required for fracture, high strain hardening increases the energy required to produce failure. In the transition region and below, however, a critical stress law appears to be valid6 and a low rate of work hardening may produce superior resistance to semibrittle crack propagation. The experimental program is aimed at studying these possibilities and determining the specific influence of strain hardening on the crack propagation resistance of several high-strength materials. MATERIALS AND PROCEDURE The alloys, chosen as representative of various classes of high-strength materials, are summarized in Table I. The heat treatments evaluated along with the smooth tensile properties are presented in Table 11. Pin-loaded sheet tensile specimens were employed to determine the smooth tensile properties. A strain gage extensometer (measuring range 0.200 in.) was used at a strain rate of 0.02 in. per in. per min. The work-hardening exponents were determined from the stress-strain curves generated in the smooth tensile tests and the assumption that the portion of the stress-strain curve beyond the yield point can be described by the power relationship: where a is the true stress, P is the true plastic strain,

Jan 1, 1969

By G. E. Pellissier, C. W. Mason

Tin has long been cited as offering a classic example of polymorphism, second in repute only to the allotropy of sulphul.. The notorious "tin disease," which Cohenl has studied so exhaustively in terms of the enantiotropic transformation of tetragonal white P tin to cubic gray a tin, has apparently encouraged the expectation that one or more additional polymorphic modifications might exist. The search for confirnmntion of this idea has, as might be anticipated, led to the accumulation of a body of miscellaneous evidence, much of which would probably never have been sought, or taken seriously even by its discoverers, but fur previous assumptions. The ball apparently was started rolling iii 1880 by Trechmann,2 who reported a new modification of tin (7 tin), which was brittle and found in "hard head," a highly arsenical, slaggy material produced in a certain stage of tin smelting. A mixture of two kinds of crystals was obtained from a Cornish tin furnace, and those thought to be 7 tin were studied crystallographically. The results indicated that these crystals were rhombic and of different density from the tetragonal tin prepared electrolytically by Miller. Their analysis was given as 98.7 per cent Sn, 1.3 per cent Fe, and traces of As, Sb, Bi and S. In 1881 von Foullon4 obtained similar crystals from a Bohemian tin furnace. Headden5 examined crystals similar to those of Trechmann and von Foullon and reported them to be monoclinic, but of analysis corresponding to stannous sulphide. Later, Stevanovic,~ by goniometric measurements, proved that these crystals of SnS were really rhombic. Groth7 pictures and describes both "rhombic tin" (Fig. 9, vol. 1) ant1 stannous sulphide (Fig. 84, vol. 1); their faces and angles correspond within the accuracy of measurement. Spencers in 1921 examined the above evidence critically; lie lound similar crystals from Cornish tin furnaces, proved them to be SnS, and even was able to analyze some of Trechmann's original specimens, finding high sulphur content. (Apparently Trechmann's analysis had been based on :L second lot of crystals, not described crystallographically.)

Jan 1, 1939

By G. E. Pellissier, C. W. Mason

Tin has long been cited as offering a classic example of polymorphism, second in repute only to the allotropy of sulphul.. The notorious "tin disease," which Cohenl has studied so exhaustively in terms of the enantiotropic transformation of tetragonal white P tin to cubic gray a tin, has apparently encouraged the expectation that one or more additional polymorphic modifications might exist. The search for confirnmntion of this idea has, as might be anticipated, led to the accumulation of a body of miscellaneous evidence, much of which would probably never have been sought, or taken seriously even by its discoverers, but fur previous assumptions. The ball apparently was started rolling iii 1880 by Trechmann,2 who reported a new modification of tin (7 tin), which was brittle and found in "hard head," a highly arsenical, slaggy material produced in a certain stage of tin smelting. A mixture of two kinds of crystals was obtained from a Cornish tin furnace, and those thought to be 7 tin were studied crystallographically. The results indicated that these crystals were rhombic and of different density from the tetragonal tin prepared electrolytically by Miller. Their analysis was given as 98.7 per cent Sn, 1.3 per cent Fe, and traces of As, Sb, Bi and S. In 1881 von Foullon4 obtained similar crystals from a Bohemian tin furnace. Headden5 examined crystals similar to those of Trechmann and von Foullon and reported them to be monoclinic, but of analysis corresponding to stannous sulphide. Later, Stevanovic,~ by goniometric measurements, proved that these crystals of SnS were really rhombic. Groth7 pictures and describes both "rhombic tin" (Fig. 9, vol. 1) ant1 stannous sulphide (Fig. 84, vol. 1); their faces and angles correspond within the accuracy of measurement. Spencers in 1921 examined the above evidence critically; lie lound similar crystals from Cornish tin furnaces, proved them to be SnS, and even was able to analyze some of Trechmann's original specimens, finding high sulphur content. (Apparently Trechmann's analysis had been based on :L second lot of crystals, not described crystallographically.)

Jan 1, 1939

[A. B. Cummins, President James C. Gray, President-Elect J. W. Woomer, Past President C. E. Lawall, Eastern Regional Vice-President Donald W. Scott, Central Regional Vice-President H. C. Weed, Western Regional Vice-President Nathaniel Arbiter, Treasurer John Cameron Fox, Secretary AIME 29 W. 39 St. New York 18, N. Y. D. R. Tone, Assistant Secretary]

Jan 1, 1961

H. 0. Hofman, Boston, Mass. (communication to the Secretary*) :—The experimental demonstration by Professor H. Ries, of the fact that a mixture of clay and finely-ground flux will melt more readily than one in which the flux is less fine and therefore less intimately mixed, is very striking, and will be appreciated especially by those who have to discuss, before classes of students, fusions on a small or a large scale. The statement, that I " rather disputed" the influence of size of flux-particles on the ease with which fire-clay mixtures fused, is an erroneous inference from the paper written by Mr. B. Stoughton and myself in 1898.' We did not undertake to study the influence upon fusibility of the sizes of the particles, either of clay or flux. What we did try to find out was, whether the common practice of finely grinding raw or burnt clay, or a mixture of the two, before testing with Seger cones for resistance to heat and to fluxes, xould give the same results as if the materials were tested just as they were going to be

Jan 1, 1904

By Robert M. Yonco, Irving Johnson, Martin G. Chasanov

The thermodynamics of the cadmium-rich portion of the Pu-Cd system has been studied with a high-temperature galvanic-cell method. The partial phase diagram of the Pu-Cd system was determined. The existence of the intermediate phases PuCd11 (cubic BaHg11 structure, ao= 9.282) and PuCd6 (cubic, CeCd6 structure, a, = 15.59) was established. The existence of at least one other intermediate phase richer in plutonium was indicated. PuCd11 was found to peritectically decompose into PuCd6 and liquid at 406" * 2°C. The solubility of plutonium in liquid cadmium may be represented by the equations: (355' to 399°C) log (at. pct Pu) = 6.223 -4282T-1 (399° to 632°C) log (al. pct Pu) - 5.148 - 5277T-1 > 1.156 x 106 T-2 The free energy of formation values (kcal per mole) of the two intermetallic phases are given by the equations: (PuCd11), ?Gf= -45.9 + 35.7 x 10-3 T (PuCd6), ?Gf0- -39.27 + 25.86 X 10-3T The excess free energy (kcal per mole) of plutonium in liquid cadmium may be represented by the equation: -(-16.72 * 29.54 NPu) 10-3T in which Npu and Ned are the atom fractions of plutonium and cadmium. The thermodyanamics of the U- Cd and Pu-Cd systems are compared. THERMODYNAMIC information on systems of the actinide metals with low-melting metals, such as zinc and cadmium, is useful in the design of pyro-metallurgical processes for the purification of nuclear reactor fuels. The thermodynamics of the Pu-Zn,1 Th-Zn.2,3 U-Zn,4-5 and U-Cd6 systems have been reported. The present report on the Pu-Cd system concerns the liquidus composition in the cadmium-rich region, the characterization of the two most cadmium-rich intermetallic phases, and the thermodynamic properties of these intermetallic phases and dilute liquid solutions of plutonium in cadmium. EXPERIMENTAL Phase Studies. The liquidus composition was determined by analysis of filtered samples of the liquid phase withdrawn at a series of temperatures. The apparatus and procedure were identical to that used in the previous study of the Pu-Zn system.' Briefly. a sample of the melt was withdrawn into a tantalum tube fitted with a porous tantalum filter (30-µ pore). the entire sample dissolved in hydrochloric acid (to avoid errors due to segregation

Jan 1, 1965

(Members are urged to send in for this column any notes of interest concerning, themselves or their fellow-members.) Members and visitors who registered at institute headquarters during October A. Adiassewich, St. Petersburg, Russia. Charles W. Merrill, San Francisco, Cal. A. F. Lucas, Washington, D. C. Carl J. Trauerman, Butte, Mont. Allan J. Clark, Lead, S. D. Herbert B. Cox, Boston, Mass. Prof. Loewinson-Lessing, St. Peters- James W. Malcolmson, Kansas City, Mo. burg, Russia. A. E. Sunderhauf, Paramaribo, Dutch F. Maury Gillespie, Abangarez, Costa Rica. Guiana, S. A. M. Gardner Talcott, Irvington-on-Hudson, N. Y. D. W. Brunton, Denver, Colo. A. P. Watt, Newark, N. J. Dwight E. Woodbridge, Duluth, Minn. S. A. Taylor, Pittsburg, Pa. Alexander Fyfe, Boston, Mass. Ralph Wilcox, Miami, Ariz. Robert A. Seip, Wilkes-Barre, Pa. William J. Cox, Denver, Colo. A. J. Eveland, Boston, Mass. E. P. Ross, Duquesne, Pa. M. F. Sayre, Brewster, N. 1. H. Mortimer-Lamb, Montreal, Canada. Albert Sauveur, Cambridge, Mass. F. L. Grammer, Leesburg, Va. Robert H. Leach, Brockton, Mass. R. R. Moore, Mexico City, Mex. Steinar Foslie, Kristiania, Norway. Charles E. van Barneveld, San William A. Wong, Honolulu, Hawaii. Fran¬cisco, Cal.

Jan 11, 1913

Discussion of the paper of JOEL H. WATKINS, presented at the New Fork meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 391 to 411. H. Rims, Ithaca, N. Y.-It is interesting to contemplate to what extent the American pottery industry would be affected in case the English supply of china clay were shut off for a considerable period of time. The English deposits are very large, and are worked on a most extensive scale. They are more easily and probably more cheaply worked than our American deposits, which are of vein-like nature. The American producer of washed clay is not always as careful as the foreign miner and washer of this material, although he has improved in recent years. Our American washing plants are, furthermore, not as economical of material as it seems to me they might be, for the reason that more or less of the finest clay is often allowed to overflow, due to insufficient settling tank capacity. This fact is often shown by the milky character, of the streams into which the waste water is discharged.

Jan 5, 1915

By E. J. Ripling

A NY mechanism proposed to explain hydrogen embrittlement in titanium and its alloys must, of course, be consistent with the experimental data that characterize this embrittlement. Unfortunately, however, the mechanical behavior of hydrogen-bearing titanium, at least a-ß titanium, has not been unequivocally defined. Lenning, Craighead, and Jaffee have clearly shown that hydrogen cmbrittles a-titanium by elevating its transition temperature, probably as the result of the formation of titanium hydrides. Therefore, in these alloys, hydrogen acts like at least one other interstitial contaminant, namely, nitrogen.&apos; On the other hand, ß-titanium has been shown by these same investigators to tolerate very large amounts of hydrogen without suffering severe mechanical damage.2 Mixing these two phases, however, to form the most important class of commercial alloys, the a-ß alloys, again results in severe hydrogen embrittlement, although the mechanism by which the embrittlement is produced is not of the same type as that which causes brittleness in a alloys. Ductility damage due to hydrogen increases as the strain rate is reduced in a-ß alloys, while embrittlement in a alloys increases as the strain rate is increased, since the latter is a transition temperature behavior. Steel, like the a-ß alloys, becomes more hydrogen sensitive at slow strain rates, suggesting that the mechanism producing the embrittlement in these two metals is similar. Brown and Baldwin&apos; described the hydrogen-produced ductility depression in steel as a function of testing temperature and strain rate by defining the slope of the two surfaces that produced the depression in a three dimensional chart, Fig. 1. One of these surfaces was given by the equations (de/de)4 > 0 (de/dT) < 0 [1] while the other was defined by the pair of equations Surfaces of the type given by Eq. 1 are suggested in two ways. One is an embrittlement mechanism wherein the diffusion rate of hydrogen is competitive with the rate at which the material is being deformed, as suggested by the planar pressure theory of Zapffe and his co-workers.&apos; The other is the diffusion controlled extension of Orowan&apos;s theory on delayed fracture in glass by Petch and Stables.&apos;&apos; Surfaces of the type given by Eq. 2 are also compatible with a mechanism of pressure build up in voids, according to de Kazinczy,&apos; since the solubility of hydrogen in the metal increases with testing temperature so that as the temperature is raised, the pressure in the voids is reduced. Kotfila and Erbin recently presented some data on the dependence of ductility on testing temperature and strain rate for the a-ß 3 pet Mn complex alloy at four different hydrogen levels.H Although data were presented for only three testing temperatures at three different strain rates, their results indicated that surfaces of the types defined in Eqs. 1 and 2 are produced in the alloy when the hydrogen level is sufficiently high—200 and 300 ppm—Fig. 2. Jaffee and his co-workers presented data on a number of different a-ß alloys which indicated the existence of surfaces of the type described by Eq. 2, but the ductility recovery at low temperatures as given by Eq. 1 was not found." In an attempt to aid in crystallizing this description of the ductility dependence of hydrogen-bearing a-ß alloys, tests were conducted by the author on a-ß titanium 140A with three different hydrogen contents. The tensile properties of two as-received rods and one vacuum annealed rod* were obtained over a range of testing temperatures and strain rates as shown in Figs. 3 and 4. Hydrogen analyses were made by the Battelle Memorial Institute on four pieces of the rod whose properties are shown as solid circles in Fig. 4. The hydrogen content of these pieces, taken at widely spaced intervals within the rod, were 280, 270, 289, and 270 ppm, indicating that the hydrogen content within a single as-received rod was quite uniform. One of the broken test pieces whose properties are shown in Fig. 3 as solid circles was also analyzed, and found to have a hydrogen content of 310 ppm. The analyses obtained on two of the vacuum annealed specimens were 92 and 170 ppm.

Jan 1, 1957

By AIME AIME

WEDNESDAY night, by long tradition, is al- ways set aside for the annual dinner, even when, as it was this year, it is Ash Wednesday. Whether the somewhat smaller attendance than last year is attributable to that cause, the unexpectedly long persistence of business depression, or whatever may have been the reason, it was a joyous occasion, and the grand ball-room of the Commodore Hotel was as completely filled With diners as * was consistent with com- fort. In the half hour before the dinner was actually served the guests assembled in an adjoining room and not only exchanged greetings but proceeded along the receiving line to greet the guests of honor. The number present was so large that hardly more than half of them had been able to do this before the summons to the dining room sounded and a hearty and immediate response was made to it. Toy balloons at each plate, inflated and directed at the heads of companions or nearby friends, but which were just as likely to carom from the nose of a hurrying waiter, successfully broke the ice as well as not a few plates. It would be interesting to know whether the pleasure the guests derive from these de- vices is in part based on the all-too evident annoyance of the waiters, and what the relative quantitative relationships are.

Jan 1, 1931

By K. H. Coats

This paper presents the development and solution of a mathematical model for aquifer water movement about bottom-water-drive reservoirs. Pressure gradients in the vertical direction due to router flow are taken into account. A vertical permeability equal to a fraction of the horizontal permeability is also included in the model. The solution is given in the form of a dimensionless pressure-drop quantity tabulated as a function of dimensionless time. This quantity can be used in given equations to compute reservoir pressure from a known water-influx rate, to predict water-influx rate (or cumulative amount) from a reservoir-pressure schedule or to predict gas reservoir pressure and pore-volume performance from a given gas-in-place schedule. The model is applied in example problems to gas-storage reservoirs, and the difference between reservoir performances predicted by the thick sand model of this paper and the horizontal, radial-flow model is shown to be appreciable. INTRODUCTION The calculation of aquifer water movement into or out of oil and gas reservoirs situated on aquifers is important in pressure maintenance studies, material-balance and well-flooding calculations. In gas storage operations, a knowledge of the water movemenr is especially important in predicting pressure and pore-volume behavior. Throughout this paper the term "pore volume" denotes volume occupied by the reservoir fluid, while the term "flow model" refers to the idealized or mathematical representation of water flow in the reservoir-aquifer system. The prediction of water movement requires selection of a flow model for the reservoir-aquifer system. A physically reasonable flow model treated in detail to date is the radial-flow model considered by van Everdingen and Hurst.1 In many cases the reservoir is situated on top of the aquifer with a continuous horizontal interface between reservoir fluid and aquifer water and with a significant depth of aquifer underlying the reservoir. In these cases, bottom-water drive will occur, and a three-dimensional model accounting for the pressure gradient and water flow in the vertical direction should be employed. This paper treats such a model in detail — from the description of the model through formulation of the governing partial differential equation to solution of the equation and preparation of tables giving dimensionless pressure drop as a function of dimensionless time. The model rigorously accounts for the practical case of a vertical permeability equal to some fraction of the horizontal permeability. The pressure-drop values can be used in given equations to predict reservoir pressure from a known water-influx rate or to predict water-influx rate (or cumulative amount) when the reservoir pressure is known. The inclusion of gravity in this analysis is actually trivial since gravity has virtually no efFect on the flow of a homogeneous, slightly compressible fluid in a fixed-boundary system subject to the boundary conditions imposed in this study. Thus, if the acceleration of gravity is set equal to zero in the following equations, the final result is unchanged. The pressure distribution is altered by inclusion of gravity in the analysis, but only by the time-constant hydrostatic head. The equations developed are applied in an example case study to predict the pressure and pore-volume behavior of a gas storage reservoir. The prediction of reservoir performance based on the bottom-water-drive model is shown to differ significantly from that based on van Everdingen and Hurst&apos;s horizontal-flow model. DESCRIPTION OF FLOW MODEL The edge-water-drive flow model treated by van Everdingen and Hurst1 is shown in Fig. la. The aquifer thickness b is small in relation to reservoir radius rb. water invades or recedes from the field at the latter&apos;s edges, and only horizontal radial flow is considered as shown in Fig. 1b. The bottom-water-drive reservoir-aquifer system treated herein is sketched in Fig. 2a and 2b. Here the aquifer

By D. E. Norquist, J. E. Moeller

The results of wear on marked balls, 4, 31/2, 3, and 2 in. diam are given. All balls were forged steel of practically the same chemical analysis and hardness. The results indicate that balls in a given mill for a given length of time will have equal diameter losses, regardless of size.

Jan 6, 1950

By J. C. Lee

This investigation considers the penetration of a crack through an interfacial boundary separating two materials. The interface is assumed to be an imperfect bond characterized by frictional resistance and the cracks are assumed to be pressurized. The formulation is achieved through the use of complex variable methods together with the application of dislocation solutions. Results are given in the form of dimensionless variables that represent the injection of an incompressible liquid.

Jan 1, 1984

By R. L. Frantz, R. W. Bouman

The authors investigated the comminution of quartz and limestone mixtures in a ball mill, showing that the distribution modulus of a comminuted material is the same whether it is ground separately or as part of a mixture. Analysis of the ground products indicates that quartz and limestone consume energy during ball milling in proportion to their mass fraction in the mixtures. Recently Schuhmann&apos; made a significant contribution to comminution theory by proposing that complex comminution operations comprise the summation of many individual comminution events. By means of the single comminution event hypothesis, Schuhmann derived the Charles energy-size reduction relationship by considering that fragments of every particle crushed during a single impact have a size distribution characterized by the Schuhmann size distribution. In this paper, the size reduction of mixtures of solids in ball mills is analyzed by considering that size reduction occurs as many single comminution events. If a mixture of two materials is being ground in a ball mill, each successful impact of a ball with a particle of one material should yield an assembly of particles whose size distribution is characteristic of that material. Considering both materials to follow the Schuhmann size distribution equation, the size distribution of material 1 in the product is

Jan 1, 1962

By A. Goldberg, T. E. Tietz, J. E. Dorn

INTRODUCTION THE concept that the flow stress for plastic deformation of metals in the work hardening range is a function of the instantaneous values of the strain, strain rate and test temperature was promulgated by Ludwick1 many years ago. This thought has been more or less a guiding principle throughout the immediate period of development and growth of mechanical metallurgy. It has been tacitly assumed or knowingly applied to many investigations on the plastic behavior of metals. Spurred by the theoretical interest and practical importance of the plastic behavior of metals, many investigators have attempted to determine empirical, semi-empirical, and theoretical equations2-18 relating the flow stress with the strain, strain rate, and temperature. Although the applications of such equations have been extensive, the experimental verification of the existence of a mechanical equation of state is weak. Furthermore, some of the available evidence on plastic flow appears to suggest that no simple functional relation between stress, strain-rate, strain and temperature can exist. The mechanical equation of state demands that [a = a(e, E, T)[I]] Where o = true stress = load/instantaneous area e = true strain = In Instantaneous gauge lengths initial gauge length e = true strain rate T = temperature] This formulation implies that [da] is an exact differential. Therefore the flow stress (o) is a function of the instantaneous values of the strain (e) the strain rate (e) and the temperature (T), independent of the previous mechanical or thermal history. Having reached a certain strain, strain rate, and temperature, by any path whatsoever, a definite and fixed value of the flow stress should be obtained. One check on the validity of the mechanical equation of state is easily obtained. Consider the following three tests on the stress-strain curve at constant temperature: [A. Strain at rate [ei] B. Strain at rate i2 C. Strain at rate [Ei] to [ei] and continue test at i2] A graphical representation of possible results of such tests are shown in Fig I. If, for strains greater than [el], test (C) data coincide exactly with the data from test (B), as shown in Fig Ia, a limited verification of the mechanical equation of state is obtained for the range of strain rates from [ii] to [e2]. But if the data from test (C) differ from those of (B) beyond strain [el] where the strain rate is changed from [e,] to [€2i] the mechanical equation of state is not

Jan 1, 1948