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By R. Schuhmann

PROBLEMS in expressing, interpreting, and using size-distribution data recur in many phases of mineral dressing; therefore it is desirable that size analyses be expressed in such a form, either numerically or graphically, that comparisons can be made readily. The size distribution of comminuted material is a result of a specific physical operation on the material and therefore should be governed by some definite physical principle, or cause-effect relation. Although this principle has not been discovered, it has been found that the size distribution of comminuted, homogeneous solids may be expressed by relatively simple mathematical equations. Two equations in particular, proposed by Gaudin1 and by Rosin and Rammler,2 respectively, have stood out, both having wide demonstrated ranges of application. The form and the method of application of the two appear almost irreconcilably different on the surface, but, as will be shown, they are asymptotic in the fine sizes when expressed in the same units. This paper gives the results of a further study of the Gaudin and Rosin-Rammler relations, made with the object of developing a form of size-distribution equation that will be more usable and more significant-particularly in comminution studies, both for interpreting the nature of size distribution and for evaluating surface. The work is summarized in the following: I. An equation relating cumulative per cent finer to particle size in the fine sizes is derived from Gaudin's original equation. That equation relates weight per cent retained on one size and through the next larger size in a geometric series of sizes to size (of the retaining screen, for example). 2. Comparisons with Gaudin's equation and with the Rosin-Rammler equation show that the cumulative equation applies to the fine sizes of all size distributions that fit either of these earlier relations, and, furthermore, has some advantages over each. 3. A simple graphical method of surface calculation based on the cumulative-equation plot is evolved and illustrated. 4. Additional confirmation of the cumulative equation was obtained in the more severe test of sizing down to the limit of a sedimentation balance a sample of jaw-crushed quartz. The equation was closely followed over a 20o-fold range in size, from approximately 0.4 mm. (35 mesh) down to 0.0023 mm. (2.3 microns), the lower limit of the size analysis made. There is no indication that the equation will not hold further to well below 2.3 microns. 5. Calculations of the surface produced in the jaw-crushing test mentioned above showed that at least 8o per cent of the total new surface was on particles finer than 35 mesh (about ½ 5 of the crusher setting). The minus 35-mesh portion was only

Jan 1, 1940

By GERALD H. HUTTON

SINCE the inception of dredge mining, the attention of engineers and operators has been directed primarily toward mechanical improvements and refinements calculated to, reduce operating costs and to increase recoveries. The result has been to develop an efficient excavating and value-saving machine, which, in some instances, has an actual capacity of 15,000 cu yd. per day. Steel hulls and superstructures minimize the risk of destruction by fire and lengthen the life of the plant. Dredges now restore, to some extent, agricultural possibilities to mined ground. Large buckets, with correspondingly heavy parts, are able to handle heavy wash and massive boulders. Mechanical weaknesses have been strengthened. The use of manganese steel in bucket lines and tumblers permits the application too the bank of a digging force that can be withstood only by solid material, such as rock, cement or frozen ground. Various alloys of steel have been applied to certain duties and experiments in their heat treatment are still progressing. Haulage by tractor or truck is in common use. Discarded and worn steel parts are repaired or rebuilt by the use of the oxy-acetylene flame and the arc-welding machine. Gold and platinum saving is more efficient, although still subject to improvement. Dredging for tin ore is in successful operation. Crews are now highly specialized and experience has developed improved methods of work; particularly in the manipulation of dredges to build levees of tailings and to leave open waterways where desired. To sum up by the distribution of overhead expense over several units, ground under favorable conditions can now be dredge-mined for 5)2 c. per cu: yd., in spite of the increase in cost of supplies, power, and labor during, the past few years. Improvements in prospecting methods, however, have not kept pace with mechanical developments. Standard practices of ; testing ground today produce only wide approximations of values; although they obtain information concerning the character of the deposit and bedrock. It is interesting to note that few important changes in the methods of ten years ago are .to be recorded; the latest comparisons between pros¬pecting results and mined recoveries-have been at such variance as to cause confusion to the operator, and, in a degree, the sacrifice of the confidence of the capitalist. On this account, and because the growing scarcity of dredging ground. demands closer calculations on the part of the engineer, this appeal for collaboration and

Jan 1, 1921

By AIME AIME

DESTRUCTION of the plants, machines, utilities, tools, materials, and other essentials for peacetime living penalizes not only the owners of the materials destroyed, but the world as a whole. Specifically, the fundamental fallacy of any proposal for the in- discriminate destruction of the German industrial system is that it fails to differentiate between the wartime and the peacetime economy of the Reich. We are for one simple, clear objective-an effective industrial means to keep Germany from starting another war. This objective should not be con- fused, especially before the war is even won, with the appropriate punishment of Germany or with the international arrangements for the long future to be made around the peace table by the representatives of the Allied Nations after victory is achieved. This paper, therefore, does not deal with broad, complex postwar questions of diplomacy and international policy. "Unconditional surrender" implies disarmament of the German armies, the surrender of all arms, munitions, air- planes, and other ordnance material in stock piles or in process. It also should include the elimination of all German war production facilities, such as ordnance plants, munitions plants, and submarine works, and the control of raw materials required by war industries.

Jan 1, 1944

By AIME AIME

DREAMS do come true at times, although it is evidently better to believe in engineers than to "believe in fairies" if most dreams are to be translated into fact. It was a fine dream that David H. Moffat had when he projected a railway directly west from Denver; a dream of opening a new empire in northwestern Colorado, and of quickening transportation from the Middle West to the Pacific slope. But Moffat had been a miner and had become a banker. He knew that dreams, untranslated into works, benefit no one and pleasure only the dreamer, so he employed an engineer, H. A. Sumner, to study and plan the route to be followed by the rails. Previous main lines had run to the north, the Union Pacific, or the south, the Santa Fe. The Denver and Rio Grande, it is true, wriggled its way bravely across Colorado but, in order to reach a point 74 miles in an airline west of- Denver, travelled 281 miles following two canyons and crossing Tennessee Pass at 10,240 ft. Valuable as such a road is, it could never accomplish what Moffat had in mind. It was known that no low pass could be found directly west of Denver but up to 9000 ft. the topog-

Jan 1, 1925

By Charles Will Wright

Brief descriptions of the occurrence of the various deposits of strategic minerals then known in South America are published in "The Mineral Deposits of South America," by B. L. Miller and J. T. Singewald, 1919; in "Ores and Industry in South America," by H. F. Bain and T. T. Read, 1934; and in many publications on the individual countries. To give a gen.era1 idea of the situation today and possibilities for future output of strategic minerals in several of the countries, the following notes are offered. All tonnages are in metric units.

Jan 1, 1940

By George A. Laird

I. INTRODUCTION. THIS old and once famous district played, through its enormous production of silver and gold, an important part in the history of the State of San Luis Potosi. According to a pamphlet prepared under the direction of the Governor of the State, Sr. Don Blas Escontria, and presented to the visiting members of the Institute during the Mexican meeting of 1901, this district is situated 20 km. east of the city of San Luis Potosi, in a range of mountains of moderate height, extending 135 km. N. and S., and 16 km. E. and W.; and the mineralized area hitherto developed is about 600,000 sq. m. The history of the district,. as given by the record dated 1778, and formerly kept in the San Francisco convent, says that it was discovered in 1575 by Sr. Don Pedro Irarte, and adds that the city of San Luis Rey de Francisco del Potosi received its name (in allusion to the famous Potosi mines in Bolivia) by reason of the remarkable productiveness of its gold- and silver-mines in the first period of their exploration, during which they paid to the Crown, as " quintos " (the fifth part of the product), $97,000,000, as appears from the accounts of the royal treasury. The amount of the quientos paid during the " bonanza period " of 80 years was $72,000,000. The larger sum first mentioned probably represents a longer series of years. But either will suffice to indicate the great wealth of the mines. In 1663, the decadence of the industry began with the caving¬ in of several mines, concerning which the record of 1778, al¬ready cited, says, in substance, that on Good Friday one of the owners in the enterprise, in view of the unfavorable prospect of a lawsuit in which he was engaged, set fire to the timbers supporting the underground galleries and workings of the San

Jan 1, 1905

By Frederic P. Dewey

(New York Meeting, February, 1912.) By the old method of determining platinum in ores and bullion, the silver-alloy first obtained in the regular course of assay is parted in strong sulphuric acid and the residual metal weighed. This is re-alloyed with silver by a second cupellation and parted in nitric acid, the residual metal being again weighed. Any difference shown between the two weighings is assumed to be, and is called; platinum. Sometimes it is so, and if any considerable amount of platinum be present, there will be a decided difference between the two weighings; but a slight difference is no real evidence whatever of the presence of platinum. On the other hand, the second weight may equal or possibly exceed the first, even when traces of platinum are present. Again, other members of the platinum group may go into solution in nitric acid more or less. If present, these would be called platinum and escape detection. The method does not provide any direct tests whatever as to the presence or absence of platinum. It is often indecisive, and sometimes jives erroneous results. It is, therefore, quite unsatisfactory. Being called upon many times to determine platinum in a wide variety of materials, particularly when present in very small amounts, I have realized the disadvantages and defects of this old method. In an article on the solubility of gold in nitric acid, 1 I have briefly outlined a method of gathering a little gold out of a solution containing much silver, which furnishes the basis of

Apr 1, 1912

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By AIME AIME

ON THE occasion of the eightieth birthday of Captain Robert W. Hunt, the Iron and Steel Committee of the Institute, desiring to commemorate the great contributions made to the steel industry by Captain Hunt during his long career, conceived the idea of a Hunt Medal to be awarded annually by the Institute for meritorious contributions to the art of making steel. The project was received enthusiastically by all to whom it was proposed, especially by Captain Hunt's partners and employees who considered it their right, and asked for the privilege of -. - raising the necessary funds within their own circle. This was agreed to, and the Institute has received from them $7500 as an endowment fund to provide an annual award, and $1000 for the expenses of providing of medal.

Jan 1, 1920

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 B. W. Frazier

Jan 1, 1882

THE committee in charge of arrangements for the meeting of the Institute in September has com-pleted its program. The headquarters of the meeting will be at the Palace Hotel, San Francisco, and the registration committee will be at the hotel all day on Sunday, Sept. 24, and from 8 a.m. until noon on Monday. On Sunday afternoon, automobiles will be available for sightseeing trips around the city. Monday will be devoted to technical sessions. In the morning, there will be sessions on Mining and on Iron and Steel; in the afternoon, sessions on Mining and Milling. At these sessions, in addition to the papers mentioned in the tentative list printed in August, there will be presented three papers on the geology, mining and milling of the Comstock lode; one on the Aztec mine, Baldy, N. M.; one on the Colombian oil fields; and one on charcoal precipitation of cyanide solutions. The luncheon on that day will be Dutch Treat, for men only, at the Engineers Club. On Monday evening, there will be an informal buffet supper at the home of F. W. Bradley. On Tuesday morning, a party of 50 men will leave for Hetch Hetchy. During the four days of the trip, the party will see the Priest tunnel and earth dam under construction by steam-shovel and hydraulic-fill methods, the Big Creek shaft and tunnel, early intake power plant and tunnels and the Hetch Hetchy dam under construction. For those who remain in San Francisco, Tuesday will be "San Francisco Day." There will be motor trips to the Presidio, Cliff House, Golden Gate Park, and other points of interest, and shopping trips to Chinatown. On Wednesday, "University of California Day," the party will be guided through the university by members of the Mining Association, the affiliated stu-dent society, and will see the Greak Theatre and not-able buildings. Thursday will be "Leland Standford, Jr. University Day." Automobiles will leave the Palace Hotel at 10 a.m., and will return from the university at 4.30 p.m. Friday has been reserved for trips to the Selby Smelter, to Mt. Tamalpais, or to other points of interest. Arrangements will be made to visit the mines or gold dredges in California, if members desire to do so, but such trips must of necessity be considered special trips and arrangements will have to be made to suit the convenience of the individual or party. The Golf Committee will make arrangements for those who wish to play golf.

Jan 9, 1922

By A. S. Yue

It was deemed desirable to obtain an understanding of the vacuum desulfurization process. McKechnie1 has reported that the sulfur content of nickel- and cobalt-base alloys is reduced in vacuo. Keverian and Taylor2 have observed that vacuum melting causes desulfurization of iron-carbon-silicon alloys. Garnyk and samarin3 have desulfurized transformer steel by vacuum treatment. Experiments were conducted in order to investigate the desulfurization of liquid iron under reduced pressures, and to establish the effect of some alloying elements, and various crucible materials. A vacuum-induction furnace of 50-lb capacity was used. The charge was Armco iron. Silicon was added as 90 pct ferrosilicon, carbon as electrode graphite, and aluminum as high-purity aluminum metal. Magnesia and silica crucibles were used, their inside diameters were 5 1/2 and 5 3/8 in., respectively. The temperature was measured with an optical pyrometer and it was held at 1600 1 15°C. Samples were withdrawn with quartz tubes of 6 mm ID, without disturbing the furnace atmosphere. Pressures were measured with an alphatron gage. The experimental results are shown in Fig. 1. They indicate that: 1) Sulfur can be removed from liquid iron alloys by vacuum treatment; 2) The desulfurization is enhanced by the presence of silicon, carbon, and aluminum, all these elements increase the activity of sulfur dissolved in liquid iron;4 3) The pronounced effect of silicon indicates that probably a volatile silicon sulfide is formed, Alcock and Richardson5 have observed a similar phenomenon; 4) The same rate of desulfurization was obtained when the metal was contained in either magnesia or silica crucibles. Dr. J. Keverian has contributed many discussions and recommendations. M. S. Sutliff has helped in conducting the heats. The permission of General Electric Co. for this publication is gratefully acknowledged.

Jan 1, 1960

By Eugene A. Stephenson

NUMBER of noteworthy events in the petroleum industry may be reported for 1941, of which the most spectacular was doubtless the rise in the daily rate of crude-oil production to a peak of approximately 4,300,000 barrels. This enormous daily rate did not ensue from the furor of flush pools but represented for the most part merely a slight additional daily delivery from many wells that had previously been operated on a more restricted basis, in line with good conservation practice and also from the adroit increase in the number of days per week by the Texas Railroad Commission. Another important fact was the increase in price throughout the Mid-Continent area from the static level of $1.02 for 36°, A.P.I., crude, to $1.17 per barrel. Efforts to elevate the price above this point have met with severe opposition from the O.P.A.. as has also a similar effort by the PennsyIvania Crude Oil Producers' Association, but the vastly increased costs for materials and labor may shortly give the industry the enhanced price which it has long deserved.

Jan 1, 1942

By Edward H. Bzirdick

THE territory under particular consideration in this article comprises portions of La Plata and Montezuma Counties, situated in the southwestern corner of Colorado, and around the base of the La Plata Mountains. (See Fig. 1.) In southeastern Utah and northeastern Arizona there are several mountain systems whose origin and structure are practically identical with the La Platas so that ore occurrences found in the latter can be hopefully looked for in the former. With this assumption, there is an area around the laccolithic ranges which offers promise for a successful exploration for gold ores. Ore occurrences of the Silverton, Telluride, Rico, or Ouray Districts will not be discussed, although in these areas the Mesozoic sediments are more or less involved within the ore-bearing complex. These have been intensively studied and developed. The idea is to set forth what my mining experience has been within the largely unaltered . Mesozoic horizon which remains around the extreme bases of the La Plazas. This, until recent years, has been almost entirely neglected by prospectors and operators and, so far as similar territory in Utah and Arizona is concerned, so remains.

Jan 1, 1934

By Fred P. Dewey

IN preparing material for the exhibit of the National Museum at the New Orleans Exposition in 1881, it was decided to attempt to photograph the interior of a coal-mine, in order to get a strictly truthful representation of a thick coal-seam, and to show incidentally the methods of mining. While we have many drawings, both mechanical and artistic, illustrating the subject, they are not satisfactory for these purposes, simply because they are drawings. Aside from this, much interest attaches to pictures of inaccessible places, and the enlarged copies (30 inches by 40 inches) of the photographs we succeeded in obtaining, have attracted a large amount of attention from the visitors to the Museum. The Kohinoor colliery, Shenandoah City, Pa., was selected as most suitable for the attempt, principally on account of the fine exposure of the Mammoth bed, and the comparatively level character of the workings, in that colliery. This is one of the many anthracite-mines of the Philadelphia and Reading Coal and Iron Company. A detailed section of the fiftyfoot or Mammoth bed in this colliery is as follows: Feet. Inches. 1 0 Clod. 1 7 0 Coal. 1 0 Slate. Top Split. 8 0 Coal. 1 6 Slate divider.* 6 0 Coal. 1 0 6 Slate. 2 6 Coal. 0 5 Slate. 1 8 Coal. 1 2 Charcoal. 5 0 coal. 1 0 Bone and Coal. „ „ Coal. [ Bottom Split. 0 6 Bone and Slate. 3 0 Coal. 0 10 Bone and coal. 1 2 Coal. 0 2 Bone. 4 4 Coal. 0 1 Bone. 0 8 Coal.

Jan 1, 1888

By T. P. Floridis

It was deemed desirable to obtain an understanding of the vacuum desulfurization process. McKechnie1 has reported that the sulfur content of nickel- and cobalt-base alloys is reduced in vacuo. Keverian and Taylor2 have observed that vacuum melting causes desulfurization of iron-carbon-silicon alloys. Garnyk and samarin3 have desulfurized transformer steel by vacuum treatment. Experiments were conducted in order to investigate the desulfurization of liquid iron under reduced pressures, and to establish the effect of some alloying elements, and various crucible materials. A vacuum-induction furnace of 50-lb capacity was used. The charge was Armco iron. Silicon was added as 90 pct ferrosilicon, carbon as electrode graphite, and aluminum as high-purity aluminum metal. Magnesia and silica crucibles were used, their inside diameters were 5 1/2 and 5 3/8 in., respectively. The temperature was measured with an optical pyrometer and it was held at 1600 1 15°C. Samples were withdrawn with quartz tubes of 6 mm ID, without disturbing the furnace atmosphere. Pressures were measured with an alphatron gage. The experimental results are shown in Fig. 1. They indicate that: 1) Sulfur can be removed from liquid iron alloys by vacuum treatment; 2) The desulfurization is enhanced by the presence of silicon, carbon, and aluminum, all these elements increase the activity of sulfur dissolved in liquid iron;4 3) The pronounced effect of silicon indicates that probably a volatile silicon sulfide is formed, Alcock and Richardson5 have observed a similar phenomenon; 4) The same rate of desulfurization was obtained when the metal was contained in either magnesia or silica crucibles. Dr. J. Keverian has contributed many discussions and recommendations. M. S. Sutliff has helped in conducting the heats. The permission of General Electric Co. for this publication is gratefully acknowledged.

Jan 1, 1960

By Krahmann, Rudolf

THE following is an account of a survey undertaken to test the possibility of outlining a kimberlite pipe by magnetouietric methods. Kimberlite is a basic igneous rock closely related to melilite-basalt or alnoite, which occurs either in the form of volcanic plugs or as dikes intruded into rocks of various types and geological ages up to and includ¬ing the Lower Cretaceous. The famous diamond mines of South Africa are all in kimberlite pipes and these pipes are probably the original source as well of the vast alluvial deposits found in various parts of the country. The pipe chosen for this experiment is one that ' occurs on the farm Goedgevonden No. 20, about sixteen miles north of the village of Klerksdorp and ninety miles southwest of Johannesburg. Some prospecting has been done on this pipe and diamonds were produced from it but not in paying quantities. The magnetometric survey was made in June, 1932, by R. Krahmann and H. Wallisch and the results are shown on the accompanying plan. On the plan are shown also the boundaries of the pipe as exposed at the surface and details in regard to the surrounding foundations. These are taken from a geological survey made at a later date by W. Beetz, of Johannesburg.

Jan 1, 1935

By J. Gurland, A. Gangulee

The cracking of silicon particles embedded in an aluminum matrix occurs progressively over the range of plastic deformation of the composite specimen. The fracture probability of the particles increases with increasing particle size and decreasing silicon contents. The crack orientation tends to be perpendiculay to the direction of the maximum tellsile strain. An example of a direct association between matrix slip and particle cracking is shorn. ALUMINUM-SILICON alloys of commercial compositions fail by ductile fracture in three stages:' I) initiation of cracks in the silicon particles, 2) growth of cracks into cavities, and 3) rupture of the aluminum matrix separating the cavities. The present work is concerned with the first stage: the initiation of cracks in the silicon particles. EXPERIMENTAL PROCEDURE Aluminum samples with 2.8, 6.1, 9.6, and 13.2 vol pet Si, respectively, were cast from commercial al- loys. Machined tensile specimens (2 in. gage length) were annealed in air at 1000°F for 100 hr, and then pulled at a strain rate of 0.025 per min. The grain size (average linear intercept) of the aluminum matrix was 0.24 and 1.6 mm in the 6.1 and 13.2 pet Si alloys, respectively. The particle size of silicon in alloys of one composition (6.1 pet Si) was varied by either modifying the castings with 0.15 pet Na or prolonging the annealing time. The average particle size was measured by linear and planar analysis, assuming spherical particles of uniform size. The particle sizes and compositions of all samples are tabulated in Fig. 8, together with the identifying symbols used in the graphs. The respective numbers of broken and unbroken silicon particles were determined from metallographically prepared longitudinal sections by counting a total of approximately 2000 particles per sample. EXPERIMENTAL RESULTS 1) Crack Initiation During Deformation as Function of Composition. Nominal stress-strain curves of four specimens of different compositions, but approximately equal particle sizes, are presented in Fig. 1. The fraction of broken particles, P (no. of broken particles/ total no. of particles), is shown in Fig. 2 as function of true stress and in Fig. 3 as function of nominal strain. The last point of each composition line in Fig. 2 rep-

Jan 1, 1968

By A. G. Weber, R. L. Ledbetter, A. L. Hicks

A procedure which makes use of both analog and digital computers has been developed for predicting the pressure-production behavior. of water-drive reservoirs. The electric analyzer is used for matching the past pressure and production history of the reservoir and inferring the physical characteristies of the aquifer. When the history has been matched, a .set of base curves called influence functionce" are derived and the future behavior of the reservoir is calculated from these curves. INTRODUCTION Electric analog methods are particularly well-suited for complex water-drive problems. Like all other methods of analyzing water-drive reservoirs, however, analog methods are subject to certain limitations. One of the more obvious and serious of these results from inaccurate or insufficient knowledge about physical characteristics of the reservoir and aquifer. However, it is not insurmountable because the unknown characteristics can usually be inferred from the reservoir's previous behavior. Simons and Spain have shown that even with scant reservoir data and limited production history, electric analyzer studies can provide useful and reliable results. Aside from this limitation on analyzer predictions, the main disadvantage has been lack of a technique for keeping predictions abreast of latest production forecasts. Pressure behavior of a reservoir depends on the rate at which fluid is withdrawn; it is therefore necessary to specify the future withdrawal schedule before the future pressure behavior can be calculated. Conventionally, the electric analyzer predicts pressure behavior for a specific production schedule. If this schedule is abandoned in favor of some new one, as is frequently the case, either the study must be rerun or results adjusted in some manner. The usual procedure is to predict pressures for several different forecasts covering a wide range of production rates. Pressures for specific rates other than those studied can then be approximated by interpolating between the analyzer predicted curves. However, reliability of this type of prediction is doubtful. This paper describes a technique for predicting future behavior of water-drive reservoirs that retains all advantages of electric analyzer analysis and eliminates the main disadvantage. That is, the analyzer is used conventionally to infer unknown reservoir parameters from the pressure history, but not to predict the future behavior directly. Instead, a derived set of base curves, called influence l'unctions, can be used to calculate future behavior for any production schedule.