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Jan 1, 1924

INTRODUCTION TO PROBABILITY THEORY The mathematical theory of probability provides the foundation for the interpretations and inferences that can be made from statistical techniques. Probability theory is a broad field of study in itself, and can only be touched on here in order to provide the necessary back- ground for a more complete understanding of statistical analysis. Probability is concerned with the outcome of random events. It had its beginnings in the theory of games of chance which were of great interest to European mathematicians during the last half of the 17th century. The outcome of a random process or experiment is defined as an event. The collection of all mathematical points associated with each event is called the sample space for an experiment. Consider a random experiment having a finite number, n, of possible outcomes, some of which have a characteristic A. What is the probability that A will result from a single

Jan 1, 1980

H. Van F. Furman, Denver, Colo. (communication to the Secretary): There are some statements in Dr. Carpenter's interesting paper which appear to require explanation, if not modification.

Jan 1, 1901

By C. J. Bier, J. F. O?Keefe

THIS study was carried out with copper because it represents the simplest form of sintering, in that but one metal is involved and all reactions occur in the solid state. [ ] The present work will cover three variables affecting the sintering process; namely, briquetting pressure, sintering temperature and time in hot zone. Although strength and dimensional changes were observed, this is primarily a metallographic study of the sintering process in copper. The term "sintering" should be understood to mean the process by which the metal powder particles of the compact become united into one body. MATERIAL USED The copper powder used was made from reduced copper oxide, and is typical of a grade used for the mass production of parts formed of metal powders. The screen analysis of the powder was as follows: [ ] The minus 325-mesh analysis was made by using a Roller Air Analyzer.1,2 The apparent density is here defined as the weight per cubic centimeter of the [ ] loose, unpacked powder as measured with the Hall flowmeter. The value for the powder used was 2.57 grams per cubic centimeter.

Jan 1, 1944

By W. E. Wrather

DURING the war the mineral industry, and metal mining in particular, extended itself more than any other to attain the limit of its productive capacity. Likewise, probably no other industry went quite so far toward jeop¬ardizing its own economic future through depletion of material reserves. Once we looked to Europe for most of the manufactured goods we needed. Our own limited mineral requirements were easily supplied from mines near the Eastern seaboard. With expansion and industrialization, our mineral needs increased in proportion, and the centers of mining activity moved westward to Michigan, Wisconsin, Minnesota, and the Tri-State district, where seemingly inexhaustible high-grade deposits of iron, copper, lead, and zinc ores were opened and rapidly developed.

Jan 1, 1946

By THOMAS LEONBRD WATSON

INTRODUCTION. IN a paper read by title at the Washington meeting of the Institute, May, 1905,1 discussed at considerable length the geological relations, node of occurrence, and the genesis of the lead- and zinc-ores of the Virginia-Tennessee region. The present paper treats of the purely economic phases of the zinc-ores of the district; such as methods of mining the ores, their preparation and treatment. The Albemarle county mines and plant were discussed in the paper referred to above, and will not be considered here. METHODS OF MINING. Until very recently the mining of lead- and zinc-ores in Virginia was limited wholly to the surface belt of weathering. The mode of occurrence and the character of the ores to be mined were such as to demand the employment of methods used in mining secondary concentrated ores. Accordingly, a system similar to that practiced in mining brown iron-ores was employed, being modified to meet the changed conditions. Oxidized or Soft Ores.-Up to the present time practically all the ore mined in the Virginia district has been of the oxidized or soft type;-the silicate, calamine, and the carbonate, smith-sonite; largely the former, which has been localized and concentrated at only slight depths below the surface. Because of the extreme irregularity with which the limestone weathers when stripped of the overlying residual clay, it presents a roughened surface of large and small irregular "chimneys"

Mar 1, 1906

By C. W. Parmelee

THE ideal fuel for burning ceramic wares is the one that, among other characteristics, has little or no sulfur. For that reason wood was long considered the most desirable fuel but its high cost has practically eliminated its used except in regions where it is very abundant or other circumstances warrant its choice. The fuels commonly employed are natural and producer gas, oil, and coal. The last named is undoubtedly the most important, not only in this country but abroad. Occasionally anthracite is used but the larger part is bituminous. The quality of the coal used depends on the kind and the value of the products being manufactured. For some materials, such as common brick, hollow block, etc., the quality of the coal is of less importance than in the manufacture of polychrome terra cotta, pottery, porcelain, etc. It is obvious that in burning clays that contain notable amounts of pyrite, marcasite or gypsum, as is the case with many common clays, the sulfur content of the fuel is of much less importance. The permissible amount of sulfur in the coal used will depend on the kind of product being manufactured. "A good sample' of coal commonly used in pottery ovens has something like this quantity of sulfur." PER CENT. Total sulfur 1.20 Sulfur in the ash 0.11 Volatile sulfur a 1.09

Jan 9, 1919

By John B. Hastings

THE origin of the watery vapors of vulcanism has always been an object of interest and speculation to the seismologist, and as theories of the genetic origin of ore-deposits have of late years been pretty well narrowed down to the expiring forces of plutonic action, the same question has had a lively interest for mining engineers and geologists, as is well shown by the discussions of the subject in our Transactions. The important part taken by volcanic emanations in the origin of pegmatites and quartz-veins, described in my paper, Origin of Pegmatite,1 and their latent power to concentrate into useful deposits such scattered gold as occurs in the Hartsel granite, make a discussion of their derivation but a natural third and final step. It is conceded that enormous amounts of vapor accompany volcanism, though perhaps we are apt to forget that steam has 1,700 times the volume of water, besides which the column seen over Vesuvius and other volcanoes is greatly mixed with air; the immensity of such volumes compared with solids and liquids is shown by the experiment of Gautier, who, by heating dessicated granite to 100° C., evolved from it uses 20 times, and steam 90 times, its own volume. Dana appraised the average amount of water left in ordinary rocks as 2.5 per cent. T. M. Read estimated that the Mississippi river carries to the sea annually 150,000,000 tons of rock material. If these Mississippi sediments, as deposited, contained 20 per cent. of water, it would be 600,000,000 cu. ft., or 4,500,000,000 American gallons, annually. Allowing the vapor suspended over a volcanic cone to be mixed with 80 per cent. of air, this amount of water converted into steam would replenish anew, every 9 min., a column 15,000 ft. high, 2,000 ft. in diameter at the base, and 10,000 ft. at the top. Read's estimate is only half of the amount given in a more recent and probably correct one .2

Jan 5, 1908

By L. D. Fetterolf, G. T. Mahler, W. M. Peirce, R. K. Waring

UNTIL recently, the only commercial method of producing magnesium has been fused salt electrolysis, despite a considerable amount of experimental work on the direct reduction of magnesium oxide. In this early work, a number of investigators demonstrated that magnesium oxide would react with any one of several reducing agents to produce magnesium vapor, but that the mixture of magnesium oxide and reducing agent must be heated to a high temperature even in a vacuum. In particular, it was demonstrated that silicon and aluminum are effective reducing agents and that when either of these is used the magnesium vapor can be condensed to massive metal. In spite of this knowledge, no successful commercial reduction process was developed, at least in this country, because of the operational difficulties imposed by the requirement of high temperature and vacuum and because of the high cost of the reducing agent. The outstanding experimental work done by Pidgeon, who carefully reviewed all of the known methods of making magnesium and then selected ferrosilicon reduction, overcame some of the operational difficulties. The process developed by Pidgeon comprises briquetting a mixture of calcined dolomite and reducing agent, pre-heating the briquets to about 600°C. in an externally heated alloy retort, reducing the MgO with silicon in an evacuated horizontal alloy retort heated externally to about 1150°C., and condensing the magnesium vapor to a solid in a cold extension of the retort projecting beyond the fr6nt of the furnace. A major advantage of Pidgeon's process is that the retort is not cooled down between charges. Earlier investigators had used apparatus that necessitated cooling and reheating of the retort between charges. Early in January 1942, when the War Production Board was considering the Pidgeon process for quickly increasing the production of magnesium, The New Jersey Zinc Co. offered to have a research investigation of the process carried on, with the hope of assisting in its further development. This offer was accepted, and a two-retort pilot plant was built at Palmerton and put in operation on Jan. 29, 1942. An intensive investigation of certain phases of the process was carried out in the ensuing four months. This investigation was completed in the last part of May 1942, and the pilot plant was then shut down. Subsequently, The New Jersey Zinc Co. was requested to have further development work done on the process, and a more extensive investigation was undertaken in August I942 under contract with the War production Board and under the super- vision of the War Metallurgy Committee. This paper describes the phases of the investigation that are thought to .be

Jan 1, 1944

By J. C. Swartz

Measurements of the effect of precipitation stresses on the solubility of cementite (Fe3C) precipitates in a iron are reported. Solubilities were determined from measurements of the Snoek relaxation due to interstitial carbon after quenching from various equilibrium treatments. Stress-free precipitates were obtained by a spheroidizing treatment of vacuum-melted Fe 0.06 wt pet C. Subsequent equilibration treatments were designed to suppress nucleation of other precipitates. The results for stress-free cementite give a heat of solution of 14.8 i 0.2 keal per mole and an entropy change of 1.1 i 0.2 eu in the temperature range 400" to 715°C. Comparison with previous data indicates that the heat of solution increases about 6 keal per mole as temperature increases from 700" to 1000°C. Data on self-stressed cementite in quench-aged specimens of Fe 0.013 wt pet C indicate 1) an apparent heat of solution of 12.1 i 0.4 keal per mole in the range 280" to 690°C, 2) a strain energy of- 1.1 keal per mole Fe3C accompanying precipitation at 280°C, and 3') a gradual decrease in the strain energy of precipitation with increasing equilibration temperature. In com-parison with 2 and 3 the strain energy calculated for an isotropic model is 1.7 keal per mole Fe3C. The lower values obtained from the experiment indicated substantial stress velaxation by dislocation motion. WHEN a supersaturated solution of carbon in a iron is aged at temperatures in the range 200o to 700oC, the carbon clusters by interstitial diffusion and forms cementite (Fe3C) precipitate particles. Unstressed cementite has a volume per iron atom 9 pet higher than that of a iron;' hence, cementite precipitate particles are usually under pressure from the iron matrix. The pressure would tend to increase the solubility of cementite in iron.' This report describes anelastic measurements of the solubilities of self-stressed and stress-free cementite in a iron. Previous determinations of the cementite solubility are summarized in Table I. The method of cementite formation for each reference was studied to ascertain the state of stress of the cementite. The results judged to be for stress-free and stressed cementite are distinguished in the table. In the next section an estimate of the stress effect is obtained which is clearly too small to account for the large difference between the previous results in parts A and B of the table. THEORETICAL Let AGO be the standard free-energy change of the reaction Fe3C (eem.) = 3Fe (a) + C (in a) [1] in the absence of stresses. Since cementite precipitates appear to be rather pure10 and the carbon is so dilute in the iron,8 the cementite and iron of Eq. [ I] for the stress-free case have essentially unit activities and the activity of carbon equals its atom fraction xoC Then the stress-free equilibrium is expressed by RT In XoC = -?GO 121 To first approximation the change in the chemical potential of carbon due to the precipitation stresses equals the elastic strain energy W accompanying precipitation of a mole of cementite.2 Hence, in the presence of the precipitation stresses the equilibrium is described by RT In x sq = -?G° + W [3] where xsC is the mole fraction of dissolved carbon in the stressed case. An approximate value of W can be obtained from analysis of the inclusion problem in elasticity theory. The inclusion is a small portion of the matrix phase which has suffered a transformation while still imbedded in the matrix. In the absence of the constraint of the matrix the transformation would be equivalent to a uniform dilational strain eT. Both the matrix (a) phase and inclusion (0) phase are assumed to be homogeneous, isotropic materials. When the a and 0 phases have the same elastic moduli, which is approximately true for iron and cementite,11 the total strain energy per mole ß is12 2µVß(eT)2(3 +4 µx)-I [4]

Jan 1, 1968

By Peter Greenfield, Paul A. Beck

Thirty binary systems of vanadium and chromium group transition elements with second and third long period transition elements were explored in regard to the intermediate phases formed. It was found that the phases predominating in these systems are s, AB type with ordered a-tungsten or C8 structure, close-packed-hexagonal with small unit cell dimensions and, finally, phases isomorphous with 1-manganese. IN recent years, considerable information has become available concerning the intermediate phases in binary systems of the transition elements. Thus, the s phase has been found to occur in most of the binary systems of vanadium, chromium, and molybdenum with the group of elements manganese, iron, cobalt, and nickel.' It was observed that, while the rr phases formed by chromium with manganese, iron, or cobalt possess a considerable temperature range of stability, particularly in the Cr-Co system, the corresponding s phases with molybdenum are limited to a temperature range of less than 400" above about 1200°C. Goldschmidt' reported v phases of tungsten with iron and cobalt, and these are apparently stable only at (and above?) 1400°C." Exploratory work in this laboratory with Fe-W and Co-W alloys of approximately 60 atomic pct W annealed at 1300°C did not produce X-ray patterns suggesting the presence of a phase. It appears then that the phases of iron and cobalt with the chromium group elements decrease in stability as the two components are chosen from long periods further removed from each other. From the available information, it might be concluded that the controlling factor is the increasing difference in atomic radii between the components. In contrast to the a phase, the phases formed by iron and cobalt with chromium group elements' are stable only when the latter have large atomic radii (molybdenum and tungsten); the corresponding phases with chromium do not occur. When the difference in atomic size becomes still larger (r,/r,, approaching the ideal value of 1.225), the u and p phases are replaced by Laves phases (AB,), as in the alloys of iron and cobalt with columbium," tantalum." and titanium."-" However, atomic size certainly cannot be the sole determining factor, since, for instance, in contrast to the very stable (Mo, Co)p phase, no such phase occurs in the Mo-Ni system even though the atomic diameters of cobalt and nickel are nearly the same. Similarly, chromium and cobalt form a a phase in a wide temperature range," but the corresponding s phase in the Cr-Ni system is missing. It has been shown that the composition of the u phase in various binary and ternary systems of transition elements in the first long period may be correlated in a fairly quantitative manner with the number of electron vacancies. The influence of electronic structure is probably present also in binary and ternary phases' and to some extent, apparently, even in Laves phases." " Although the absence of phases in the Cr-Ni and Mo-Ni systems has not as yet been explained on the basis of electronic structure, it appears reasonable to suspect a connection. One of the great difficulties in arriving at well founded rules in regard to the alloying behavior of transition elements lies in the lack of reliable information concerning the details of their electronic structure in the metallic and alloy form. The theoretical penetration of this field appears to be beset by very considerable difficulties, even when the complications due to alloy formation are disregarded. Another great source of uncertainty is the scarcity of phase diagram information even for binary systems of the transition elements so that only a very limited basis is provided for generalizations as to the occurrence of intermediate phases. For instance, very few binary phase diagrams of second and third long period transition element systems have so far been published. The present work was undertaken in order to survey the various types of intermediate phases occurring in 30 binary systems of elements of the group vanadium, columbium, tantalum, chromium, molybdenum, and tungsten with the elements rhenium, ruthenium, rhodium, palladium, and platinum. For most of these binary systems phase diagrams are very incompletely or not at all known, as will be further reviewed.*

Jan 1, 1957

By John S. Johnson, Thomas Fraser

SIZING is the process of separating mixed particles into groups of particles all of the same size, or into groups in which all particles L range between certain definite maximum and minimum sizes. In coal preparation, sizing is generally accomplished by passing the coal over screens. Separation by differential settling in air or water currents has been adapted to the special field of separating very fine sizes, and these processes are in commercial use to a relatively small extent in the coal industry. Separation with screens is a very old industrial practice. Agricola 1 described the use of screens for ore treatment in the middle ages. In the literature of the British coal industry references were made to the screening of coal as early as 1589, but the practice of extensive sizing for the market did not become general until the last half of the nineteenth century. In America, the practice of sizing developed first in the Pennsylvania anthracite region, beginning with the use of rakes2 in the mine working places to recover coarse coal. This mining procedure left the fines in the mine. Preparation outside the mine started with the installation of stationary cast-iron plates with 4 to 6-in. square holes. The run-of-mine coal was dumped upon the platforms, the large pieces of rock were picked out by hand, and the large lumps of coal were broken with hammers. The term "breaker," which still applies to the anthracite-preparation plant, originated with this practice, but the term is no longer descriptive of the entire function of the plant. In 1884, the first power-operated anthracite coal breaker3 was erected by Gideon Bart at his colliery at Wolf Creek near Minersville, Pa. This plant utilized a system of rolls for breaking the coal and revolving screens for sizing. The plant was driven by a steam engine. It could handle

Jan 1, 1943

By M. W. Ditto

THe conversion of the beehive coke plants, in this country, to byproduct plants has been slow, because the coal supplies were near the centers of the steel industry. With the growth of this industry, especially with its development around Chicago, it became necessary to transport large tonnages of coal from the eastern districts and then convert it into coke. The losses due to transportation costs were partly offset by the value of the byproducts recovered. To save the transportation costs, it was desirable that the coal deposits of Indiana and Illinois be utilized. This coal had always been classified as non-coking; it was also considered unsuitable for the metallurgical field because of the high ash and sulfur contents. The conditions, however, were promising enough to start experimental and development work, which crystallized in the design of the Roberts coke oven. The fundamental features of most coke ovens, with respect to the application of heating gas and the recovery of byproducts, are the same and, in the last few years, the tendency has been toward the better application of heating to the walls, higher thermal efficiency, and, by the control of heating conditions, the increase of byproduct yields. Structural features also have been improved and the use of high-grade refractory material has allowed the use of higher temperatures with the resulting higher rated capacity per oven per day. Great improvements have been made in both recuperators and regenerators, particularly with reference to the individualizing of each oven with respect to its adjacent oven, so that each can be operated as a unit if desired. The highest development of the flue type of oven has been applying individual regenerators for the recovery of waste heat. After some research work, it was found that the high-volatile Illinois coals could be utilized for coke by obtaining the better application and control of the heating conditions in the oven. Most of this high-volatile coal that had been used gave a good coke structure under certain conditions. The fact that coke was occasionally made from this coal, demonstrated the possibiity of making coke from it at all times pro-

Jan 1, 1923

By M. W. Ditto

THe conversion of the beehive coke plants, in this country, to byproduct plants has been slow, because the coal supplies were near the centers of the steel industry. With the growth of this industry, especially with its development around Chicago, it became necessary to transport large tonnages of coal from the eastern districts and then convert it into coke. The losses due to transportation costs were partly offset by the value of the byproducts recovered. To save the transportation costs, it was desirable that the coal deposits of Indiana and Illinois be utilized. This coal had always been classified as non-coking; it was also considered unsuitable for the metallurgical field because of the high ash and sulfur contents. The conditions, however, were promising enough to start experimental and development work, which crystallized in the design of the Roberts coke oven. The fundamental features of most coke ovens, with respect to the application of heating gas and the recovery of byproducts, are the same and, in the last few years, the tendency has been toward the better application of heating to the walls, higher thermal efficiency, and, by the control of heating conditions, the increase of byproduct yields. Structural features also have been improved and the use of high-grade refractory material has allowed the use of higher temperatures with the resulting higher rated capacity per oven per day. Great improvements have been made in both recuperators and regenerators, particularly with reference to the individualizing of each oven with respect to its adjacent oven, so that each can be operated as a unit if desired. The highest development of the flue type of oven has been applying individual regenerators for the recovery of waste heat. After some research work, it was found that the high-volatile Illinois coals could be utilized for coke by obtaining the better application and control of the heating conditions in the oven. Most of this high-volatile coal that had been used gave a good coke structure under certain conditions. The fact that coke was occasionally made from this coal, demonstrated the possibiity of making coke from it at all times pro-

Jan 1, 1923

?AARONSON, ALFRED E , Vice-Pres , Mid-Co Petroleum Co, Mid-Co Bldg, Tulsa, Okla '18 ABADIE, EMILE R, Min Engr Address wanted '76 || ABADILLA, QUIRICO A, Geol Dept, Cia Mexicana de Petroleo "El Aguila," S A, Edifico "El Aguila," Esq, Calles Aurora y Comercio, Tampico, Tamaulipas, Mexico '20 ABBOTT, CLARENCE E, Gen'l Supt, Iron Mines Div, Tenn Coal, Iron & R R Co, 1405 Minnesota Ave, Bessemer, Ala '04 ABBOTT, LOUIS BENJAMIN, Chief Engr, Consolidation Coal Co, Elkhorn Div, Jenkins, Ky '15 ABBOTT, ROBERT R Met Engr, Peerless Motor Car Co, Cleveland, Ohio '12 ABE, ASAKA Fujita Min Co, Dojima, Osaka, Japan '14 ABEEL, GEORGE H, JR, Cons Min Engr, 635 St Paul Ave, Los Angeles, Cal '18 ABEL, ALBERT E, Asst to Pres, Valley Mould & Iron Corpn, Sharpsville, Pea '19 ABEL, W D, Min Engr Forum Bldg, Sacramento, Cal '19 ABELL, O J, Pres & Treas, Abell-Howe Co, 332 South Michigan Ave, Chicago, Ill '19 ABERNATHY G E Willow Springs, Mo '20

Jan 1, 1923

By Oliver C. Ralston

THE two chemical compounds, natural sodium carbonate and sodium sulphate, in their anhydrous condition are dealt in as "soda ash and "salt cake”-names from an earlier day that are not as precise as the present accepted terminology. Once a large part of the sodium carbonate recovered was in the ash of seaweed, so it was logically called soda ash, and the corresponding potassium carbonate, once mainly recovered from wood ashes, was called potash. The term "salt cake" was applied to the sodium sulphate resulting from interaction of sodium chloride with sulphuric acid or sodium bisulphate, to form hydrogen chloride gas and an anhydrous cake of sodium sulphate. It was called "salt cake" and also "glassmaker's salt cake" because much of it was used in the production of glass. The two salts occur in nature in a variety of forms, but whereas an- hydrous sodium sulphate (thenardite) is fairly common, the anhydrous normal sodium carbonate, Na2CO3, is almost never found in nature. The monohydrate (thermonatrite), Na2CO3.2H2O, is seen occasionally, but it is never a major constituent in natural "soda" deposits. The high solubility of normal sodium carbonate is one reason for this. While both compounds occur widely in brines, the solid salts found in nature are usually trona (Na2CO3.NaHC03.2H2O) and thenardite (Na2SO4). The natural brines containing workable quantities of the two sodium salts are largely found in the arid and semiarid portions of the western United States and other countries. The classical discussion of the resources of these brines are those of Clarke,5 Chatard.4 Packard,19 Gale,11 and Wells.28 From North Dakota to California and from Arizona to the Canadian provinces of Alberta and Manitoba, saline lakes, dried-up lakes, playas, and similar land-locked depressions contain accumulations of saline matter. Sodium chloride is the predominant salt but some of the lakes contain predominantly either sodium carbonate or sodium sulphate. Often sodium carbonate

Jan 1, 1949

By Tegner C. Johnson

Just a few years ago, my company was referred to as the Marion Steam Shovel Company. Though we still make shovels, both two and eight-crawler types, the eight-crawler stripping shovel appears to have been replaced by the walking dragline for overburden removal and in some cases for the mineral as well. The walking dragline appeared in the coal fields in the early 1930's. It is popular because it can cope with overburden depths in excess of 100 ft and with blasted sedimentary rock, all at an O & O (ownership and operational) cost of ±10[c] per bank cu yd (bcy).

Jan 10, 1974

By J. D. Rice, P. L. Wearden, W. L. Hensou

Solutions to the unsteady-state partial water-drive reservoir performance problem can be obtained through the use of analogue computers or high-speed electronic digital computers. The solutions that have previously been resolved for use on digital computers, however, demand a knowledge of the aquifer parameters. Generally, the analogue computers now in use do not require this knowledge. A solution is presented herein where the aquifer performance, expressed in terms of difference equations, is related to the reservoir performance as expressed by the modified Scbiltbuis material-balance equation. A numerical procedure for a medium-sized digital computer also is presented in which a solution to the set of equations defining the aquifer and reservoir performance is obtained and the aquifer parameters (permeability and sand thickness) are automatically optimized while simultaneously matching the known pressure behavior. Predicted pressure behavior can be calculated using rates from any assumed future production practice. The procedure provides an output format which presents the cumulative, incremental and average rate of natural water influx, the per cent gas-cap expansion, the calculated reservoir pressure, the measured reservoir pressure, and the difference between the measured and calculated pressures. Results of a test problem are presented in comparison with results obtained by the Bruce Analyzer, Ohio Oil Co. 's Pace General Purpose Analogue Computer, and Sun Oil Co.'s Single-Pool Electronic Reservoir Analyzer. These results indicate that unsteady-state reservoir perlormance for a single-pool system can be adequately simulated by a numerical method employing a digital computer and that the special-purpose analogue computer can be supplanted by this method. INTRODUCTION The numerical approach to the unsteady-state partial water-drive reservoir performance problem heretofore has been limited in that solutions have been resolved only for certain fixed parameters. Also, prior to the advent of high-speed electronic digital computers in the last few years, calculations were so tedious and time-consuming that they ordinarily were neglected, or some other means of obtaining the solutions were used. The analogue approach had been used for obtaining solutions to the transmission-of-heat problem and, consequently, means were developed for applying the electrical analogue to the unsteady-state reservoir performance problem. Bruce submitted a paper for AIME publication in Sept. 1942, in which he described an electronic device (now called the Bruce Analyzer) for analyzing the water-drive performance of any reservoir, based on either steady or unsteady-state flow characteristics. 1 Sun Oil Co. adopted the analogue approach in 1949 and now has two special-purpose high-speed electronic reservoir analyzers in use.2,3 Two main features of Sun's analyzers are (1) the high repetitive rate of reproducing the entire history of reservoir performance cyclically a number of times per second, and (2) the elimination of the necessity of knowing the properties of the associated aquifer. Since the advent of larger and faster digital computers, the possibility of incorporating this second feature into a numerical approach appeared feasible. Previous work has been done and material published covering the application of numerical methods to the behavior of the pressure with respect to time at any point in an associated aquifer? However, the aquifer parameters must be known from some source. The material presented in Ref. 4 has been used to a great degree in developing the numerical method described herein. DIFFERENTIAL EQUATION AND BOUNDARY CONDITIONS The problem of simulating the performance of a reservoir and the associated aquifer is to determine the characteristics of the aquifer such that the

By H. H. Kellogg

Available high-fernperatzwe equilibrium measurements and other thermochernical data have been critically reciewed for sulfation reactions of the type: Recommended values for log K and ?Fo as junctions of temperature are given for thirty-six suck reactions involving twenty-six different metals. Methods of calculation and choice between conflict-ing data are discussed. SELECTIVE sulfation now enjoys a considerable renaissance as a metallurgical unit process due, in large part, to the available of the fluid-bed re- actor—a device capable of the close control of temperature and gas composition necessary for a successful sulfation process. An additional need, however, if sulfation chemistry is to be approached in a scientific manner, is a reliable body of data on the equilibrium and kinetics of sulfation reactions in simple and complex systems. This paper offers a critical review and compilation of equilibrium data on pure sulfates (simple systems). The last such review, by K. K. Kelley in 1935:30 has proven itself most useful, but the existence of many new data makes necessary a re-evaluation of the available information. METHODS OF CALCULATION For a simple sulfation reaction such as MS04(c) = MO(c) + SO3 [1] there are two approaches one may take toward establishing the value of ?Fo or K as a function of

Jan 1, 1964

By Elmer W. Pehrson

OPINION seems widely divergent as to where we stand with respect to future mineral supply. From some quarters we hear that the United States is about to become a "have-not" nation and about to experience the evil consequences such a situation would entail. Others claim that we are still a treasure house of stored-up mineral wealth, the surface of which barely has been scratched. The data to be presented here support the conclusion that neither of these viewpoints is correct and that we are far from exhaustion of those mineral resources that are basic to our industrial economy. However, exhaustion is well advanced in a number of important subsidiary minerals so that we can no longer drift along with the easy-going philosophy that the earth will provide. The time has come when we must recognize the true situation and do something about it.

Jan 1, 1945