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By T. S. Spicer, C. C. Wright, R. G. Bowman

In recent years considerable publicity has been given to the problem of atmospheric pollution by fuel-burning equipment. Legislation has been stimulated and smoke ordinances have been enacted, the provisions of which show a definite trend toward stricter control of the emissions not only from the stacks of industrial fuel users but also from the chimneys of domestic consumers. As a result of war conditions, some slackening in the enforcement of these ordinances may be noted, but this is only a temporary expediency caused by the changes necessary in the distribution of the nation's fuel supplies and difficulties in securing the necessary equipment. Previous trends may be expected to continue in the postwar period. Largely because of the consumer demand for automatic heat, but partly because of the legislation against smoke emission, there has been a marked increase in the use of domestic underfeed stokers with the past decade. When correctly adjusted and operated, these units reduce the smoke emission materially, so that even the high-volatile bituminous coals may be burned with little or no emission of objectionable smoke. Unfortunately, however, the use of the domestic underfeed stoker introduces another problem; namely, fly-ash. Production of Fly-ash The term "fly-ash" is a misnomer, since the fly material is generally a mixture of small carbonaceous particles varying from green coal to coke, and inorganic particles ranging from fluffy ash to small particles of fused clinker. For want of a more comprehensive name, however, the term fly-ash is used throughout this paper to include all the fly material. Even with hand-fired furnaces a certain amount of fly-ash is produced, which necessitates periodic cleaning of the boiler flues or furnace radiator, the smoke pipe, and occasionally the chimney itself. With stoker operations the amount of fly-ash is increased many fold, because of the higher velocity of air travel through the fuel bed. Frequently the amount of this fly-ash attains such proportions as to constitute a definite nuisance to the householder and his neighbors and distracts very materially from the otherwise automatic or semi-automatic performance of the stoker. Virtually all the boilers and hot-air

Jan 1, 1944

By Y. Fukunaka, Y. Kondo, Z. Asaki, S. Nakashita

The pyrite smelting process in which about half amount of sulfur is recovered from pyrite by thermal decomposition in an oxygen-free high-temperature combustion gas flow in the flash smelting furnace is being conducted at Kokkola Works in Finland. A mathematical model of this process was developed, and the rates of thermal decomposition and fusion of suspended sulfide particles in the reaction shaft of furnace was calculated. This model is thought to be appropriate because of a fairly good coincidence of the calculated length of reaction zone with the shaft height of the furnace at Kokkola Works. The calculated reaction zone in which the thermal decomposition and fusion of sulfide particles occur becomes longer when pyrite particles of larger sizes are fed. The feeding rate of pyrite particles and the gas velocity at the nozzle exit are also the important operating factors. These two factors are closely related to the volume fraction and the residence time of suspended particles in the gas stream, and the optimal combined levels of these factors at which the length of reaction zone becomes minimal were obtained.

Jan 1, 1976

By Bauer. Larry G.

The vast coal reserves in the Wyoming, Montana, North and South Dakota region are sufficient to supply the total energy needs of the United States for several hundred years. Not only is there an abundance of this sub-bituminous and lignite coal available, but it is easily obtainable by strip-mining . The overburden varies from several feet to several hundred feet. This western coal has yet another asset, namely, a low sulfur content. Whereas eastern and midwestern coal has a sulfur content of 2.5%, the upper Great Plains coal contains sulfur in the 0.5% range. The importance of the sulfur content of the coal is a direct result of federal government emission standards for sulfur dioxide (SO2). Hand (1) points out that "sub-bituminous coals and lignites have a propensity for retaining this sulfur in the ash under certain conditions which is not evident in higher rank coals." This would tend to reduce further the SO2 concentration in the combustion gases of boilers. Western coal is no panacea, however, in that it is far removed from most population and industrial centers. Furthermore, the moisture content of the coal varies from 20 to 40%. This moisture is almost exclusively inherent, that is, it is chemically and physically bound to the organic matter of the coal. It is believed that the water forms a part of the coal structure perhaps as water of hydration of organic salts or organic acids, perhaps by hydrogen bonding, or perhaps by simple adsorption (2). The primary market for this coal is the electric power industry. Lesser markets will be as coke for the steel industry and possible as a raw material for coal gasification and coal liquefaction plants.

Jan 1, 1983

By N. R. Tipman, G. E. Agar, L. Paré

The flotation chemistry of the commercial INCO matte separation process was investigated. The slow cooling of Bessemer converter matte forms discrete phases of Cu2S and Ni3S2 and a Cu-Ni alloy. After magnetically removing the alloy, the Cu2S and Ni3S2 are separated by flotation at pH 12.4 (saturated lime) using diphenyl guanidine (DPG) as both collector and frother. DPG has been used exclusively in this flotation process because of its unusual selectivity for copper minerals. The surface product resulting from chemisorption of DPG onto theCu2S was identified as the double salt CU(DPG)2SO4.CU(DPG)2(OH)2. The adsorption followed Langmuir behaviour up to a monolayer coverage. In the absence of DPG, the rapid adsorption of oxygen by Cu2S in flotation pulps was observed. The surface product was identified as the insoluble basic copper sulfate CuS04.3Cu(0H)2 with the production of sulfate ion. In the presence of DPG, the oxidation reaction appears to be suppressed. The frothing properties of DPG and commercial frothers were compared. DPG is not a powerful frother. Batch flotation tests confirmed that DPG is a highly selective collector when compared to most sulfhydryl collectors.

Jan 1, 1976

By C. A. Stetefeldt

The hacienda Sauceda is one of the largest and finest haciendas in the vicinity of the City of Zacatecas, Mexico, and is said to reduce ores by the Patio process more cheaply than any other establishment. It receives its supply of ore from the San Acacio mine. This mine has been for some time, like most of the Zacatecas mines, out of bonanza, and yields, at present, ore of rather low grade. The silver occurs principally as silver-glance, ruby-silver and native silver, associated with pyrites of iron and copper, and some galena and zinc-blende, in a gangue of pure quartz, which takes the form of amythyst whenever the ore is of high grade. All the ore, as it comes from the mine, is broken by hand into small pieces, and sorted before it is delivered to the hacienda. Here it is first crushed dry in Chili mills, and then ground wet in arrastras to an impalpable powder. The sulphurets not decomposed in the patio process are separated in the settlers from the tailings and concentrated by hand. By roasting them in a reverberatory furnace with carbonate copperores, "magistral" is obtained. All machinery is driven by mulepower.

Jan 1, 1885

Organization Place Date 1917 American Institute of Architects Philadelphia., Pa. Dec. 26-29 American Society of Mechanical Engineers New York City. Dec. 4-7 American Mining Congress State Chapter Phoenix, Ariz. Dec. 26-29 1918 American Society of Civil Engineers New York, N. Y. Jan. 22-25 American Institute of Mining Engineers New York, N. Y. Feb. 18-21

Jan 12, 1917

By C. R. Wohrman

A melt of pure electrolytic iron with about 0.4 per cent. sulfur and 7 per cent. manganese was prepared in connection with a study of inclusions in iron. The alloy darkened rapidly when etched with a 10 per cent, alcoholic solution of nitric acid, and microscopic examination revealed the presence of a semimartensitic, semi-Widmanstättian structure (Figs. 1 and 2) closely resembling the structures found by Benedicks in his artificially prepared "meteoric iron."' The structures found by Benedicks were readily explained by the presence in his alloy of the two well-known iron-nickel solid solutions, taenite and kamacite, and of their eutectoid (?) aggregate, plessite. By analogy, one would infer the existence of similar phases in the iron-manganese alloy just described, such an inference being strengthened by the similarity displayed in many ways by nickel and manganese in their effects on iron. Iron-manganese Alloys are Regarded as Homogeneous Heterogeneity of iron-manganese alloys has not been recognized heretofore, judging from the data of standard metallographic books and those of original papers. In fact, iron and manganese are quite generally regarded as completely miscible in the solid state. Dr. Rosenhain,2 for example, writes: Alloys of group (a), of which those of gold-silver, iron-manganese, and copper-nickel are examples, when allowed to crystallize sufficiently slowly to attain their condition of final equilibrium, present a microstructure exactly similar to that of a pure metal—the homogeneous character of the molten solution is in that case so completely maintained that the microscope cannot detect the presence of any second constituent. Guillet and Portevin3 refer to the iron-manganese system as an example of the "case of metals completely miscible in the solid state."

By R. J. McNally

THERE are three primary plant nutrients—nitrogen, phosphorus, and potassium—expressed in any fertilizer compound as percent N, percent P 2 O 5, and percent K 2 O, in that order. This article will be concerned with the first two. The chief source of P 2 O 5 is phosphate rock. As found in the western states phosphate rock is essentially tricalcium phosphate-calcium fluoride (fluor-patite). As such, it is quite water insoluble.

Jan 1, 1957

By AIME

Cores must be cut in half to secure workable samples for saturation, porosity, and permeability tests. They come from the field labeled as to the type of core, well, and depth from which they came.

Jan 1, 1948

By W. Gundaker, F. C. Schwerer

Natural chromium-bearing spinels (chromites), which are used as refractory materials in basic steelmaking, are the only commercially important chromium ore and are also encountered as difficult-to-separate contaminants in ore deposits of potential economic value. Techniques for characterization and separation of ore materials frequently are dependent on the magnetic properties of the constituent minerals. An experimental program was initiated to explore the effects of temperature and of simple mechanical and thermal treatments on the static magnetic properties of several ore-grade natural chromites. Studies of the temperature dependence of the magnetic properties showed that the natural chromites, which are dilute in the magnetic ions Fe and Cr, order magnetically only at cryogenic temperatures. However, mechanical treatment in the form of crushing produces a magnetic component that is ordered at room temperature and that is of sufficient strength to alter magnetic-separation characteristics. The additional magnetic component apparently is associated with surface structures which develop during crushing and disappear after heating to above about 500°C. Preliminary studies indicate that this surface structure enhances the susceptibility of the chromite grain surfaces to gas reactions at moderate temperatures.

Jan 1, 1976

By Enrique Hauser

Discussion of the paper of ENRIQUE HAUSER, presented at the New York meeting, February, 1916, and printed in Bulletin No. 110, February, 1916, pp. 521 to 534. GEORGE A. BURRELL, Pittsburgh, Pa. Mr. Hauser determined the influence of inert gases on the properties of fire-damp mixtures, and one might take some issue with his work on the effect of hydrogen, on those mixtures. It is valuable information to have, but as far as the practical application of it goes, it is not of much significance, because one does not find it in mines, at least not in any appreciable amount. The same Fig. 1.-APPARATUS FUR DETECTING COMBUSTIBLE GASES IN AIR. thing can be said of ethylene. Ethylene is formed in considerable quantities as a product of heat reaction, but normally, in the coal mines, as a result of a great many analyses we have made at the Bureau of Mines, we cannot say that ethylene is a combustible gas found in the fire-damp in coal mines.

Jan 5, 1916

By Munroe F. Warner

As originally built, the plant of the American Zinc and Chemical Co. at Langeloth, Pennsylvania, was based upon the Joplin and Wisconsin fields as primary sources of zinc ores, the ores being the then normal jig and table concentrates. Construction incorporated standard Matthies-sen and Hegeler kilns without regenerators. With the development of differential flotation, zinc concentrates produced by that process became the basis of operation. These concentrates were very fine, upwards of 90 per cent passing a 300-mesh screen, and had a comparatively low fusing point with marked caking and crusting characteristics. Difficulties and losses quickly developed. In roasting, the ore went through a decidedly fluid state, and spills became serious. Caking and crusting on hearths was severe and dust losses throughout became intolerable. Acid recoveries dropped from the normal ton-for-ton level to 0.85 tons per ton of ore, and choking of Glover towers and acid lines became a problem. In 1926 and 1927 a two-unit sintering plant was built and placed in operation in accordance with the Baelen process for finishing desulphuri-zation with admixture of carbon. This had its beneficial effect in smelting, but the other problems remained. The problem presented was the roasting of Pecos flotation concentrates at the rate of 200 tons daily to a sulphur content suitable for finishing in the sintering plant. Specifications had to be governed by the existing acid plant of four chamber sets built in units of two, rather widely separated, and the sintering plant built in the space between the existing pairs of kilns, of which there was one on the center line of each of the four chamber sets. The problem contained elements of pioneering and experimentation. A thermal analysis and heat balance clearly demonstrated a possibility of accomplishing autogenous roasting, well worth the attempt, because of high fuel costs and resultant economies in operation of the acid plant due to decreased gas volumes and a consequent release of capacity for increasing acid production, a problem also faced.

Jan 1, 1937

By W. L. Dumoulin

A RATHER detailed description of the entire plant and leaching process was given in a paper recently presented to the Institute,1 so this paper will cover briefly only the crushing practice of the New Cornelia Copper Co. for the year, 1918. The ore, which is mined by steam shovels and loaded in side-dump cars, passes through two crushing plants. These crushing plants were constructed to crush the ore required by a leaching plant of 5000 tons daily, capacity, during a crushing period of 16 hours. The primary plant reduces to less than 3 in. (76 mm.) and the secondary plant, to ¼ in. (6.35 mm.), which is sufficiently fine for satisfactory percolation of solution through the ore in the leaching tanks, and to give good extraction. The ore is then conveyed to the leaching tanks by a system of 28-in.. (71-cm.) belt conveyors. On the way to the leaching tanks, it passes through an automatic sampling plant, where a 1-per cent. sample is taken. From the primary crushing plant, the ore is conveyed by two 36-in. (91-cm.) belt conveyors to a 10,000-ton steel storage bin, with a reinforced-concrete flat bottom. The ore discharges from the bottom of this bin onto four 20-in. belt conveyors, which deliver it to the four units of crushers in the secondary crushing plant. There is no storage bin between the mine and the primary crushing plant. The ore breaks very coarse, is very hard, and contains a great many boulders, some as large as 4 ½ by 4 1/2 by 10 ft. (1.3 by 1.3 by 3 m.). Jams form in the bowl of the coarse crusher in the primary crushing plant, as a consequence, and are freed by means of an immense steel hook operated from a 40-ton electric traveling crane.

Jan 8, 1919

By Norman Ketzlach

ANGANESE today overshadows all strategic materials in our planning for national se-curity," according to a report issued recently by the American Manganese Producers Association. By far the greater part of the manganese ore used in the United States is imported. "We have enough manganese ore in the United States to last from one hundred to three hundred years and longer, but most of the deposits are undeveloped. As in the case of copper, lead, and zinc, manganese ore, both foreign and domestic are low grade. Manganese ores have to be concentrated and processed. After being processed, domestic ores are higher grade than foreign." Most of the manganese ore found in this country, however, is not amenable to concentration by ore-dressing methods. Manganese Products, Inc. has developed a sulphurous-sulphuric acid leaching process for the recovery of manganese from low-grade, intermediate manganese ores. By the term "intermediate manganese ores" is meant those ores in which the manganese in the form of manganese oxides is found to have two different valences, usually two and four, as is probable in Mn,O, or the ore may be a mixture of manganous and manganic oxides. "Intermediate" manganese siliceous ores are ores in which the silica is a constituent of the ore and is loosely linked to the manganese by water of crystallization. This process has been carried out with the type of manganese ore found in the Olympic Peninsula of western Washington; Clough, N. C.; and Lava Hot Springs, Idaho, as well as just recently with manganese ore from Las Vegas, Nev. As far as the manganese leaching process is concerned, these ores differ primarily in the form in which the manganese oxides occur. The tetravalent manganese, the manganese existing in the dioxide form, is soluble in a sulphurous acid solution. To dissolve the divalent manganese, sulphuric acid is required. To dissolve the type of ore found in Washington and North Carolina, a mixture of both sulphurous and sulphuric acid is used. Whereas to dissolve the type of manganese ore found in Idaho and also in Montana, sulphurous acid alone is sufficient. The Nevada manganese ore is of the same type as that found in Idaho as far as the leaching process is concerned. It has long been known that manganese ores, with the exception of rhodonite, which is a true manganese silicate ore, can be dissolved readily in sulphurous and sulphuric acids.' The removal of the impurities such as silica, iron, and alumina from the resulting solution is the step that has been difficult. The process worked out by Manganese Products has been carried through pilot-plant equipment. This process has also been extended to the production of ammonium sulphate. Leaching of Ore: The manganese ore, ground to —-65 mesh is leached with sulphurous acid and sul-

Jan 1, 1951

By Norman Ketzlach

ANGANESE today overshadows all strategic materials in our planning for national se-curity," according to a report issued recently by the American Manganese Producers Association. By far the greater part of the manganese ore used in the United States is imported. "We have enough manganese ore in the United States to last from one hundred to three hundred years and longer, but most of the deposits are undeveloped. As in the case of copper, lead, and zinc, manganese ore, both foreign and domestic are low grade. Manganese ores have to be concentrated and processed. After being processed, domestic ores are higher grade than foreign." Most of the manganese ore found in this country, however, is not amenable to concentration by ore-dressing methods. Manganese Products, Inc. has developed a sulphurous-sulphuric acid leaching process for the recovery of manganese from low-grade, intermediate manganese ores. By the term "intermediate manganese ores" is meant those ores in which the manganese in the form of manganese oxides is found to have two different valences, usually two and four, as is probable in Mn,O, or the ore may be a mixture of manganous and manganic oxides. "Intermediate" manganese siliceous ores are ores in which the silica is a constituent of the ore and is loosely linked to the manganese by water of crystallization. This process has been carried out with the type of manganese ore found in the Olympic Peninsula of western Washington; Clough, N. C.; and Lava Hot Springs, Idaho, as well as just recently with manganese ore from Las Vegas, Nev. As far as the manganese leaching process is concerned, these ores differ primarily in the form in which the manganese oxides occur. The tetravalent manganese, the manganese existing in the dioxide form, is soluble in a sulphurous acid solution. To dissolve the divalent manganese, sulphuric acid is required. To dissolve the type of ore found in Washington and North Carolina, a mixture of both sulphurous and sulphuric acid is used. Whereas to dissolve the type of manganese ore found in Idaho and also in Montana, sulphurous acid alone is sufficient. The Nevada manganese ore is of the same type as that found in Idaho as far as the leaching process is concerned. It has long been known that manganese ores, with the exception of rhodonite, which is a true manganese silicate ore, can be dissolved readily in sulphurous and sulphuric acids.' The removal of the impurities such as silica, iron, and alumina from the resulting solution is the step that has been difficult. The process worked out by Manganese Products has been carried through pilot-plant equipment. This process has also been extended to the production of ammonium sulphate. Leaching of Ore: The manganese ore, ground to —-65 mesh is leached with sulphurous acid and sul-

Jan 1, 1951

By Oswald J. Heinrich

The serious objections to the Leblanc soda process may be enumerated as follows: 1st. The total loss of sulphur employed, equal to about one-third of soda produced. Various processes have been proposed to regain this sulphur, but none have come into practical operation on a large scale. 2d. The great balk of waste products, equal to nearly twice the amount of soda, which forms a serious annoyance about the works. 3d. The complicated series of operations necessary. 4th. The large amount of labor and fuel required. 5th. The prodoction of noxious gases which necessitate extensive condensing arrangements. 6th. The large capital necessary for the . erection and maintenance of the plant, These objections have long been recognized, and many attempts have been made during the last thirty or forty years, to discover and introduce a cheaper and more direct method for the manufacture of this important staple. The reaction between bicarbonate of ammonia and common salt, whereby bicarbonate of soda, insoluble in a solution of chloride of ammonium, is precipitated, has been closely studied for the last twentyfour years, on account of its simplicity and the purity of the product it affords. This ammonia-soda process is now so far developed, that while it is not in position to entirely replace the Leblanc process, yet it can successfully compete with it where the conditions and localities are favorable. The advantages of the ammonia-soda process may be summed up as follows : 1st. It is independent of the essential agent in the Leblanc process, via., sulphuric acid, and hence can be established in those localities where salt is abundant, and yet where sulphuric acid could not be made, or where it could not be transported profitably. 2d. The ammonia-soda process being a " wet" process, the evaporation of salt brines to obtain the solid salt required in the Leblanc process, is rendered unnecessary. 3d. The direct conversion of chloride of sodium into bicarbonate of soda, which can readily be converted into the maketable monocar-

Jan 1, 1879

By B. M. Larsen

In endeavoring to put the art of the steelmaker on a more scientific basis, as a means of securing closer control of the product, we must be severely critical of the basis of any theory we use. In particular, we must be careful to distinguish between factors that are primary and those of only secondary impartance. The concentration relations that determine the slag-metal equilibria, which are usually more or less closely attained, are of course of primary significance, but a, dear picture of the whole process requires that the actual rates of the several reactions be taken properly into account. At the high temperature of the steelmaking furnace, all reactions might be thought to be very rapid, but some of them in fact are not; the essential causes of this condition are important to a proper understanding of the process. This paper aims to present, and to justify, the viewpoint that the most significant reaction is the oxidation of carhon in the metal, the progress of which determines the oxygen pressure levels in slag and metal and produces stirring effects, all of which influence the course of the process as a whole. Reaction Rates at Steelmaking Temperatures General experience in reaction rates makes it almost certain that at steelmaking temperatures equilibrium is attained practically instantaneously when the reactants are well distributed in a single liquid phase —that is, in the so-called homogeneous reactions. The actual slowness of some of the reactions in the open-hearth furnace must therefore be attributed to a relatively slow rate of diffusion within the slag or metal phase, which limits the rate at which the reactants can meet each other in the liquid steel or at its surface. That the reactions can be made to go with great rapidity, by proper mixing and stirring of the reacting phases, is indicated by the following illustrations: 1. In the Bessemer process there is intimate contact between air and the whole mass of metal, and the reactions are complete in a few minutes. 2. Perrinl has demonstrated that by pouring liquid steel into slag contained in a deep ladle, and thereby producing almost a slag-metal emulsion, the phosphorus or oxygen content of the steel is adjustcd immediately. 3. Barret, Holbrook and Wood2 observed a quite rapid rate of desulphurization when powdered calcium carbide was stirred vigorously into liquid iron. 4. When a spoonful of liquid steel is poured into a. mold containing aluminum wire, the formation and precipitation of alumina occurs in the fraction of a second required to freeze the surface layer of the tiny ingot. The first three examples all show that any means of increasing the effective surface between slag and metal and promoting intimate mixture of the reacting phases, thereby obviating the limitation imposed by diffusion, will enhance the speed of the steelmaking process.

Jan 1, 1941

By B. M. Larsen

In endeavoring to put the art of the steelmaker on a more scientific basis, as a means of securing closer control of the product, we must be severely critical of the basis of any theory we use. In particular, we must be careful to distinguish between factors that are primary and those of only secondary impartance. The concentration relations that determine the slag-metal equilibria, which are usually more or less closely attained, are of course of primary significance, but a, dear picture of the whole process requires that the actual rates of the several reactions be taken properly into account. At the high temperature of the steelmaking furnace, all reactions might be thought to be very rapid, but some of them in fact are not; the essential causes of this condition are important to a proper understanding of the process. This paper aims to present, and to justify, the viewpoint that the most significant reaction is the oxidation of carhon in the metal, the progress of which determines the oxygen pressure levels in slag and metal and produces stirring effects, all of which influence the course of the process as a whole. Reaction Rates at Steelmaking Temperatures General experience in reaction rates makes it almost certain that at steelmaking temperatures equilibrium is attained practically instantaneously when the reactants are well distributed in a single liquid phase —that is, in the so-called homogeneous reactions. The actual slowness of some of the reactions in the open-hearth furnace must therefore be attributed to a relatively slow rate of diffusion within the slag or metal phase, which limits the rate at which the reactants can meet each other in the liquid steel or at its surface. That the reactions can be made to go with great rapidity, by proper mixing and stirring of the reacting phases, is indicated by the following illustrations: 1. In the Bessemer process there is intimate contact between air and the whole mass of metal, and the reactions are complete in a few minutes. 2. Perrinl has demonstrated that by pouring liquid steel into slag contained in a deep ladle, and thereby producing almost a slag-metal emulsion, the phosphorus or oxygen content of the steel is adjustcd immediately. 3. Barret, Holbrook and Wood2 observed a quite rapid rate of desulphurization when powdered calcium carbide was stirred vigorously into liquid iron. 4. When a spoonful of liquid steel is poured into a. mold containing aluminum wire, the formation and precipitation of alumina occurs in the fraction of a second required to freeze the surface layer of the tiny ingot. The first three examples all show that any means of increasing the effective surface between slag and metal and promoting intimate mixture of the reacting phases, thereby obviating the limitation imposed by diffusion, will enhance the speed of the steelmaking process.

Jan 1, 1941

By W. T. Cardwell, R. L. Parsons

This paper discusses the practical problem of estimating a single equivalent permeability for an oil reservoir, or a portion thereof, whose actual permeability varies in an irregular manner. Limiting averages for general types of permeability variation are developed, and illustrated by examples involving important, specific types of variation. Introduction The theory of the flow of fluids through porous media1"4 is becoming increasingly important in predictions of oil-reservoir behavior. In practical applications, however, reservoirs are seldom found to which simple theory strictly applies. Actual reservoirs have complicated shapes and nonuniform permeabilities and porosities. This paper discusses the problem of estimating a single equivalent permeability for an oil reservoir, or a segment of an oil reservoir, whose actual permeability varies in an irregular manner. The equivalent permeability of a reservoir segment is defined as the permeability of a homogeneous segment of the same dimensions that would pass the same flux under the same pressure drop- It is the permeability value that can be used in simple theoretical formulas to calculate the reservoir behavior. To the authors' knowledge, previous theoretical calculationst on systems of nonuniform permeability have been carried out only by Muskat'"; and he has not dealt with irregular variations, except in writing down the general differential equation for the pressure in variably permeable systems.lb In practical work, many calculations necessarily have been made to estimate equivalent permeabilities from the permeabiiity profiles obtained by core analyses. Regarding such calculations, Johnston and Sherborne6 say: Simple arithmetic and weighted averages have been tried on many wells and it has been found that, where frequent sampling has occurred, the arithmetic average is as satis- factory as a weighted average. It is possible that the application of statistical methods to the analysis of permeability data as recently presented by Law8 may prove fruitful. L,, has made a valuable contribution in showing how statistical analyses may aid in picturing the characteristics of a reservoir from those of a necessarily limited number of core samples. It is believed however that the particular problem of the estimation of equivalent permeabilities can be most directly approached from a fluid dynamical viewpoint as given in the present paper. An example is presented of the use of the conclusions herein in conjunction with Law's method. Theory In order to approach the problem of heterogeneity simply, it is interesting to consider a square block composed of four smaller, homogeneous, square blocks of porous medium, two of which have a

Jan 1, 1945

By Thomas T., Read

ALTHOUGH the first colonists in the area that is now the A United States, whether Spanish, French or English in nationality, were usually keenly interested in the possibilities of mineral wealth, it is a curious and interesting fact that none of them happened upon the mineral deposits that eventually were to make this the greatest mineral-producing country; up to 1800 it would probably have been rated as rather poor in minerals. Spanish explorers traversed the southeastern United States with- , out finding the Appalachian gold deposits that aroused so much interest in the early nineteenth century; Coronado sought in vain for the seven golden cities of Cibola; and the important gold \ deposits of California were not discovered until the political sovereignty of the region had passed from Mexico, which had held it for three centuries. The French also held Canada for nearly two centuries (and the British for another century) without finding the mineral deposits in Ontario and Quebec that now are so important. Though they knew of the copper of the Keweenaw peninsula, the lead ores. of Wisconsin and Missouri, and the coal of Illinois in the seventeenth century, these deposits were all too remote for exploitation. In the area held by Great Britain, iron smelting was planned at Jamestown as early as 1619 and was actually begun at Lynn, Mass., in 1643. The industry grew slowly, at first, but had reached considerable importance before the Revolution. Commercial bituminous coal mining began about 1750 in Virginia but anthracite mining in Pennsylvania was not started until 1800. As a result there was naturally little interest in the technical aspects of mineral prodnction here before 1800 by any except the few people who were actually engaged in it. Students of natural science were much interested in minerals, however. The activities of those who rank as geologists are so thoroughly covered in

Jan 1, 1941