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By L. A. Rapoport, W. J. Leas, C. W. Carpenter

A program of scaled flow model experiments has been undertaken to study the performance of five-spot water floods. The modeling procedures are discussed and the construction and operation of the flow models are described. The tests were specifically designed to investigate the effects of injection rate and of oil-to-water viscosity ratio on oil recovery. The areal sweep of five-spot water floods was also studied, and direct comparisons between five-spot and linear flooding behavior have been established to permir better utilizatfon of core analysis results for purposes of field waterflood evaluations. INTRODUCTION For a long time reservoir engineering procedures have been confined to the consideration of idealized, one-dimensional or linear systems.11* However, direct application of the linear waterflood mechanism to the evaluation of actual field performance is justifiable only for the purposes of rough approximation. To obtain a realistic analysis of field behavior, it is necessary to account for reservoir geometry and well distribution, and to take into consideration the configuration of the flow of fluids between injection and producing wells. In the past it has been attempted to account for the complex nature of the fluid movement in the reservoir by associating each well pattern with a certain "sweep-efficiency constant", e.g., a sweep efficiency of 72 per cent for the conventional five-spot pattern.' More recently, methods of waterflood evaluation have been improved by the introduction of variable sweep-efficiency factors, defining the areal coverage as a function of cumulative water injection and viscosity or "mobility" ' ratio.""' These variable sweep-efficiency factors, derived from miscible fluid displacement experiments, require the assumption of piston-like displacement of oil by water. This implies that only one fluid, either oil or water, is moving at any one point of the reservoir ht any moment. Such an assumption, however, is incompatible with the bulk of the experimental evidence and also theoretical considerations which indicate that usually in the area invaded by water, both oil and water are flowing in varying proportions, in accordance with the relative permeability characteristics of the porous medium. Another recent approach toward the evaluation of five-spot flooding behavior involves correlations of the areal sweep efficiency (observed in immiscible fluid experiments) with a "mobility ratio," based on the consideration of the "average" relative permeability to the displacing fluid. Combination of these correlations with a modification of the Buckley-Leverett frontal-drive equation leads to a computational procedure for predicting the recovery performance of areal water floods. While of considerable interest, this approach has no complete theoretical justification and, therefore, does not entirely clarify the features of five-spot water floods. Rigorous, theoretical treatment of waterflood behavior in two- or three-dimensional systems as encountered in the reservoir, including proper consideration of relative permeability and capillary-pressure functions, is as yet beyond the scope of analytical or computational methods. The, behavior of such water floods can, however, be studied by means of scaled flow model ekperiments, which is the approach followed in these investigations. The flow model experiments described in this paper simulate a uniform, horizontal formation of constant thickness with fully penetrating wells. The system under consideration is entirely liquid saturated and not influenced by compressibility effects, which is representative of the situation achieved after gas fill-up under practical conditions. Gravity segregation effects are assumed to be negligible, which implies a relatively thin reservoir formation and/or low vertical permeability. THEORETICAL CONSIDERATIONS For a flow system of uniform thickness with no appreciable effects of gravity segregation, the analysis of water-oil displacement can be confined to a two-dimensional treatment based on the consideration of a "slice" of unit thickness. Referring to previously established derivations," the displacement of oil by water in such a system can be described by the following, dimen-sionless equations:

By M. R. Tek, K. H. Coats, D. L. Katz

In natural gas storage operations, seasonal pressure fluctuations in the gas reservoir cause the water from the surrounding aquifer to flow into and out of the gas sand. The theory of unsteady-state liquid flow through porous media developed by Van Everdingen and Hurst' has been applied to predict the water movement into and out of the gar bubble for .several .postulated pressure cycles. Those cycles with as many pound-days above the original aquifer pressure as pound-days below, may cause the gas reservoir to slowly grow or shrink rather than hold to a constant volume. Applications to an actual field case study give the predicted gas reservoir monthly pressures and volumes as compared with the observed monthly pressures and volumes. INTRODUCTION A large number of natural gas storage reservoirs are bounded by or adjacent to large water-saturated formations called aquifers. The presence of these aquifers is usually evidenced by the production of water from wells delineating the gas-hearing sands. Some gas storage reservoirs in use today have been purposely developed on aquifers. Cyclic pressure variations in a gas storage reservoir cause water influx and efflux from the surrounding aquifer. This, in turn, results in a varying gas reservoir volume. The prediction of the effect of this aquifer fluid movement on the size and size variation of the gas reservoir can provide information valuable in the study of several reservoir engineering problems. The economics of gas storage operations are directly influenced by the influx of aquifer fluid into the reservoir since a shrinking storage reservoir requires increasing pressures for the storage of the same quantity of gas. Material balance and reserve or recovery calculations also obviously require knowledge of reservoir volume. Various other reservoir engineering calculations such as interpretation of well interference data, evaluation of physical characteristics of porous media, water coning, gas injection and pressure maintenance studies are typical problems where variations of volume due to edge or bottom-water encroachment becomes important. The solution of equations describing influx and efflux of water in the gas sand, application to gas storage reservoir behavior and interpretation of results are the main objectives of this paper. While this work was directed toward gas storage reservoirs, it applies equally well to repressuring of partially depleted oil reservoirs with an active water drive. MATHEMATICAL ANALYSIS As just mentioned, the cyclic pressure variations in an aquifer-surrounded gas storage reservoir cause water movement and varying gas reservoir volume. Prediction of this volume variation from the reservoir pressure cycles or the injection-production schedule requires adoption of a flow model, certain assumptions concerning reservoir and fluid properties, and formulation and solution of the governing differential equation. The flow model used in this study is a gas bubble located on a very large aquifer (Fig. la). Gas bubble radius and aquifer sand thickness are denoted by rr and h, respectively. Fig. lb shows the horizontal, radial two-dimensional porous reservoir attended by the unsteady, compressible motion of the aquifer liquid. Volume variation of the gas bubble is determined from aquifer water flow across the cylindrical boundary, r = r0

By D. O. Wyble

Five water-driver fields, for which pressure predictions had been made within a few years after discovery, were re-studied when four to five years of additional pressure and production data became available. It was fortnd that forecasts of the pressure in water-dri~fe reservoirs may be subject to considerable unccrtainty. Predictions car be erroneous when there is insufficient presswe history to define the cllaracteristics of the aquifer, and when there are errors in the pressure, production or geologic data. INTRODUCTION The efficient operation of an oil or gas reservoir requires that the important characteristics of the reservoir be determined soon after its discovery. It is especially desirable to evaluate the pressure-production relationship quickly, for this relationship provides a basis for deducing the type of production mechanism that is operative, and for making pressure predictions. The pressure predictions, in turn, provide a basis for calculating efficient rates of production, determining whether water or gas should be injected, etc. The importance of pressure prediction is such that forecasts should be made as accurate as possible, and the limits of error well defined. Historically, pressure forecasts for some fields have proved very accurate, while for others the forecasts were so erroneous that they resulted in the adoption of wrong, or at best, unnecessary production practices. Pressure predictions made for water-drive fields are especially subject to error. Accurate forecasting for these fields requires that much be known not only about the reservoir proper but about the adjacent water-filled rock as well. The water-containing rock, or aquifer, may extend for many miles, and often there is only meager data regarding its thickness, permeability and porosity. Much of the information must be inferred from the previous pressure behavior of the reservoir. A brief pressure history may provide little information about the characteristics of the aquifer. Hence, pressure predictions made early in the life of water-drive fields can be incorrect. The work described in this paper was done to determine the degree of reliability which can be expected of pressure predictions made within a few years after water-drive fields are discovered. Five fields, for which the original pressure predictions had been based on less than seven years' history, were re-examined with the aid of four to five years of additional pressure data. Where the predictions were inaccurate, the reasons for failure were ascertained. The studies were accomplished by use of the electric reservoir analyzer.' The analyzer was first adjusted to repeat the original pressure-production match using the same values for the various parameters as were used in the original study. Then, the actual production rates experienced during the time elapsed since the initial study were set into the analyzer, and the pressure behavior indicated by the machine for this period was compared with that which actually OCcurred. Where the pressure profile traced out by the analyzer deviated from the observed field behavior, the analyzer was readjusted to obtain a better over-all match. The old and the new solutions were compared to determine the reasons for any differences. COMPARISON OF PREDICTED RESERVOIR PRESSURE BEHAVIOR WITH ACTUAL PERFORMANCE Field A The original pressure-production match is entirely adequate as evidenced by the pressure match of the field's history subsequent to Jan., 1952 (see Fig. 1)'.

By E. G. Woodruff

The earlier struggles in petroleum geology were directed to solving the Qrigin and method of accumulation of petroleum. We are now fairly well agreed on those subjects. Most of us think that the great mass of petroleum commercially produced comes from plants or animals, or possibly from both. We are confident that the oil was not produced where it is now found but has accumulated in reservoirs of various kinds. The types of reservoirs are certainly variable but they just .as certainly follow definite geologic laws. Some of these types of reservoirs can be determined from surface study; others cannot. We know, too, that these types of reservoirs (largely structures such as anticlines, domes, and terraces) are much more widespread than the oil pools. In other words, there are many places where good sands and good structures exist but where oil is not found. It is the purpose of this paper, therefore, to attempt to analyze, from a regional standpoint, some of the conditions that control the presence or absence of oil pools and to group them in a regional way, hence the term "Petroliferous Provinces." The paper lays no claim to presenting new facts but attempts to group and classify the information that so many have expressed again and again. The essential factors for an oil field are petroleum, a reservoir material, and conditions under which the petroleum can enter the reservoir but cannot escape except through the drill holes. The paper will first discuss the source of petroleum as it occurs in definite regions, then the regional arrangement of reservoir strata, and finally the areal arrangement of structures. To have petroleum, there must be a source. Since living matter is considered the source of the petroleum, geological conditions must have been such that living organisms were abundant. Arid regions on the earth's surface have not given rise to living things in sufficient abundance to produce oil; similarly, too cold regions and saline inland lakes. The converse of this is that warm moist conditions must prevail to produce an abundance of vegetable matter. Before an area can be

Jan 1, 1921

By John Birkinbine

Much has been contributed to the Transactions of the Institute concerning the construction and operation of American blast-furnares ; but the following compilation is offered as possibly furnishing additional information upon the general features, dimensions, locations, capacities, etc., of the blast-furnaces of the United States; while, incidentally, the ores upon which they rely are noted in a general way. The paper is presented chiefly as a compilation, and the figures given are selections from most reliable sources, or averages calculated from official statistics, placed for convenient reference, with a view of assisting those who consult the Transactions in determining the present relative merits and importance of various sections of the country. The scope of the paper has been restricted to as few topics as possible, and all the details of special plants, or notable outputs have been ignored. While every effort has been made to give correct figures and data, the changes which are constantly taking place in the iron-producing industry, will, undoubtedly, by the time the paper is in print, develop some errors. It is difficult to determine which of the blast-furnace plants of the country should or should not be considered as upon the active list. A number which have not been in operation for years are still reported as active, some of which will scarcely be put in blast again, and others are handicapped so that they can only operate in times of abnormal profits. It is therefore scarcely probable that there are over 600 blast-furnaces in the United States which can properly be considered as active; but so many considerations affect the various plants, that, it being impossible to determine the exact number, I have relied upon the annual reports presented to the American Iron and Steel Association. Concerning the number of plants which could be stricken from the list, the Secretary of this Association says: "In January last (1885) we enumerated 669 furnaces, which included many stacks which had not been in blast for a very long time, and others which could not be operated except during short periods of exceedingly high prices for pig iron. We have gone over this list very carefully and have eliminated 10 anthracite, 19 bituminous, vol. xiv.—36

Jan 1, 1886

By Peter L. Swanson

A microcrack process zone is frequently suggested to accompany macrofractures in rock and play an important role in the resistance to fracture propagation. Attenuation of surface waves propagating through mode I fractures in wedge-loaded double-cantilever beam specimens of Westerly granite has been recorded in an attempt to characterize the structure of the fracture process zone. The ultrasonic measurements do not support the generally accepted model of a macroscopic fracture that incrementally propagates with the accompaniment of a cloud of microcracks. Instead, fractures in Westerly granite appear to form as gradually separating surfaces within a zone having a width of a few millimeters and a length of several tens of millimeters. A fracture process zone of this size would necessitate the use of meter-sized specimens in order for linear elastic fracture mechanics to be applicable.

Jan 1, 1984

By E. W. Steele

IN THE copper-casting department of a modern electrolytic copper refinery there are two kinds of casting furnaces: the first, or anode furnace for casting crude copper into anodes for electrolysis; the second, or refined-copper furnace for casting the cathodes resulting from electrolysis into market shapes, such as ingots, wire bars, and cakes. Both furnaces are reverberatories of practically the same general design and are operated intermittently, putting through a charge normally in 24 hours. The treatment of the copper in both furnaces is similar, in so far that oxidation followed by skimming and reduction (poling) is carried on in both; but in the refined-copper furnace, the work must be done with greater care and it is of extreme importance that not the slightest trace of impurity be introduced into the copper. The furnaces usually hold from 150 to 300 tons of molten copper, which constitutes the daily charge. Except in the case of furnaces in the Lake district, where the concentrates from native-copper ores are charged through the roof, the furnaces are charged through the side doors by charging machines similar to those used in open-hearth steel practice. In 1916, at the Perth Amboy plant, of the American Smelting & Refining Co., located at Maurer, N. J., a study was made of the possibility of firing the copper refinery furnaces with pulverized coal instead of by hand. The proposed method possessed obvious advantages over hand firing and coal was a much cheaper fuel than oil at that time. It was realized, however, that there were several objections to its use, the principal ones being the liability of increasing the sulfur content of the refined copper, and the additional slag that might be produced from the ash. The increase of the sulfur content of the refined copper was the more serious, as more than 0.002 per cent. sulfur is objectionable. In the case of the slag, any increase would be expensive as the copper in this slag would have to pass again through the entire smelting and refining process.

Jan 3, 1925

By N. F. Mott

Jan 1, 1961

By Donald L. Katz

The equilibrium constants developed by Souders, Selheimer and Brown1' have been very useful tools in predicting vapor-liquid equilibria during the past five years. Their equilibrium constants were computed by assuming ideal solutions and recognizing the deviations of vapors from ideal gas laws. The same fundamental concepts were used by Lewis and co-workers8 for predicting vaporization phenomena by means of fugacities. The equilibrium constant is defined by equation 1: y\x =K [1] in which K = equilibrium constant, y = mol fraction of a constituent in the vapor phase, x = mol fraction of the constituent in the equilibrium liquid phase. The equilibrium constants are a function of temperature and pressure and might be considered as replacing the ratio of the vapor pressure to the total pressure of Raoult's law. They may be used to compute the vapor or saturation pressure of a liquid or the dew point of a vapor for any pressure or temperature from the analysis of the mixture much as Raoult's law is used. Likewise, the quantity of a mixture that will vaporize at any equilibrium temperature and pressure and the composition of the vapor and liquid may be calculated. The purpose of this paper is to review the available equilibrium data of interest in petroleum production, to discuss the auxiliary physical properties of the hydrocarbons, and to present typical uses of the equilibrium constants. The particular applications chosen are the computation of the results of stage separation of crude oil and natural gas, the calcula: tion of a pressure-volume curve of a crude oil-natural gas mixture, and information gleaned from a consideration of reservoir equilibria.

Jan 1, 1938

By H. P. Allen

THE Achotla mill of the Cia. Minera de Peñoles is of special interest in that it is one of the few still employing the chloridization process. The ore milled comes from the Suriana mine and consists of both oxide and sulphide, from neither of which can the gold or silver be extracted by a simple cyanide treatment. The mill was built in 1927, after several years of study in the development of the process1, and operated from December of that year until October 1930. Operations were resumed in February 1935, and have been continuous since, treating approximately 5000 tons per month, while the mine is getting up to full tonnage of 6500 tons per month.

Jan 1, 1937

By Samuel H. Dolbear

THE value of a mine is basically dependent on its capacity to yield profits. Since the ore must be mined, treated, and sold, some of it in various future years, there is a risk involved as to future costs, selling price, and working conditions. It cannot be expected that the economic condition existing at the time of valuation will continue unchanged for long periods in the future.

Jan 9, 1953

By W. H. Bassett

THE modern smelting and refining of copper is distinctly an American development. The present demand for sound and perfect castings for rolling is due to the development of American industry. Prac-tically every article made from sheet metal or, for that matter, from any form of metal is made by mass produc-tion methods. Faulty material disturbs the orderly sequence of operations and in addition requires expen-sive inspection and unbearable rejection of finished product. This demand, therefore, is positive and will have to be met. Some mines produce ore that can be smelted and re-fined without the electrolytic process into satisfactory copper for the wrought metal industry, and some of these ores carry small amounts of impurities that are of use in hardening and toughening the copper. Most of the copper ore mined contains impurities that must be removed and, fortunately, precious metals which are separated at the same time make this re-moval profitable. The modern electrolytic refineries have their methods so well under control that the product meets all re-quirements without question if properly fire refined and cast. The "if" in this case is important, because there is evidence of carelessness or want of control at times in the material from some of the producers. It is nec-essary that the melted cathodes should be saturated with oxide to dispose of sulfur and that the copper should then be poled to the proper pitch or set. Sometimes statements leak out to the effect that it is unnecessary to oxidize completely the molten cathodes and a little less rabbling saves poles, which are expensive. The re-sult is that the rolling mill gets porous castings and produces seamy or slivered sheets or strips. The condition of the molds, their temperature, and the temperature of the metal are all important to good copper cakes, wedges, or wire bars. Cracked, and burned molds leave rough places and porous spots. Molds which are out of shape, or cracked, make shrink-age cracks which gap open when the castings are hot-rolled. Dampness means porosity. Drops of oil mean porous or honey-combed areas. Poor or irregular dress-ing means mold wash in the castings. Cold copper or slow pouring means cold sets.

Jan 4, 1928

By A. L. Foell

The development of the modern blast furnace began more than one hundred years ago, with the abandonment of the small hillside furnaces. Its development, especially during the past 50 years, has been accomplished through a rapid succession of enlargements and improvements. The remarkable growth in furnace output during this period is a tribute to the engineers and operators who have constantly endeavored to build larger and more efficient blast furnaces. The blast-furnace operators and their mechanical and electrical maintenance staffs have originated most of the furnace improvements as a result of their practical operating experience. Furnace Lines About 50 years ago furnaces consisted of hearths about 11 ft. in diameter, which merged into rather high flat boshes, with no cylindrical section between the bosh and inwall and no cylindrical section at the stock line. Since then the lines of the furnace invariably have included a cylindrical section above the bosh and a cylindrical section at the stock line. Notable increases have been made in both hearth diameters and furnace heights. During the past 10 years hearth diameters in new and replaced furnace stacks have rather consistently fallen within the range of 25 to 28 ft. while their heights have varied be- tween 100 and 106 ft. The lines of most large furnaces using Mesabi ores have followed a fairly uniform pattern (Fig. I) in which the principal dimensions for 25-ft. hearth furnaces are as follows: Hearth diameter............... 25 it. o in. Height of bosh................. 10 ft. o in. Bosh angle.................... 81 1/2º Diameter top of bosh........... 28 ft. 0 in. Inwall batter per foot........... 15/16 Stock-line diameter............. 19 ft. 6 in. Large-bell diameter............. 14ft. 6 in. Height from iron notch to top ring casting...................... 100 ft. o in. In determining the size of a new furnace for the replacement of an existing stack or for an addition to productive capacity, it is not possible to formulate a procedure that can always be followed. Local conditions, requirements as to capacity, available raw materials and prospects for future expansion dictate the size of such proposed improvements or additions. However, where the immediate requirements indicate a stack or furnace of a certain productive capacity, and the future prospects indicate that more capacity can be utilized, it is well to consider building the furnace ior the ultimate capacity rather than to install a smaller hearth with provision for future enlargement. The decision to build the larger hearth and stack for the ultimate capacity probably will require no greater initial investment, since the saving in the cost of brickwork will about offset the greater cost of the hearth jacket, tuyere breast and bosh bands. In the meantime. the furnace of larger hearth dimensions, while operating below its ultimate output, will yield a better coke rate and

Jan 1, 1943

By A. L. Foell

The development of the modern blast furnace began more than one hundred years ago, with the abandonment of the small hillside furnaces. Its development, especially during the past 50 years, has been accomplished through a rapid succession of enlargements and improvements. The remarkable growth in furnace output during this period is a tribute to the engineers and operators who have constantly endeavored to build larger and more efficient blast furnaces. The blast-furnace operators and their mechanical and electrical maintenance staffs have originated most of the furnace improvements as a result of their practical operating experience. Furnace Lines About 50 years ago furnaces consisted of hearths about 11 ft. in diameter, which merged into rather high flat boshes, with no cylindrical section between the bosh and inwall and no cylindrical section at the stock line. Since then the lines of the furnace invariably have included a cylindrical section above the bosh and a cylindrical section at the stock line. Notable increases have been made in both hearth diameters and furnace heights. During the past 10 years hearth diameters in new and replaced furnace stacks have rather consistently fallen within the range of 25 to 28 ft. while their heights have varied be- tween 100 and 106 ft. The lines of most large furnaces using Mesabi ores have followed a fairly uniform pattern (Fig. I) in which the principal dimensions for 25-ft. hearth furnaces are as follows: Hearth diameter............... 25 it. o in. Height of bosh................. 10 ft. o in. Bosh angle.................... 81 1/2º Diameter top of bosh........... 28 ft. 0 in. Inwall batter per foot........... 15/16 Stock-line diameter............. 19 ft. 6 in. Large-bell diameter............. 14ft. 6 in. Height from iron notch to top ring casting...................... 100 ft. o in. In determining the size of a new furnace for the replacement of an existing stack or for an addition to productive capacity, it is not possible to formulate a procedure that can always be followed. Local conditions, requirements as to capacity, available raw materials and prospects for future expansion dictate the size of such proposed improvements or additions. However, where the immediate requirements indicate a stack or furnace of a certain productive capacity, and the future prospects indicate that more capacity can be utilized, it is well to consider building the furnace ior the ultimate capacity rather than to install a smaller hearth with provision for future enlargement. The decision to build the larger hearth and stack for the ultimate capacity probably will require no greater initial investment, since the saving in the cost of brickwork will about offset the greater cost of the hearth jacket, tuyere breast and bosh bands. In the meantime. the furnace of larger hearth dimensions, while operating below its ultimate output, will yield a better coke rate and

Jan 1, 1943

By Paul R. Smith

Preparation for flotation begins with dragline mining, pumping, washing, screening, and desliming. Slimes, nominally -150 mesh material, constitute large quantities of phosphate and water which are a disposal problem. Older techniques involve sizing at about 35 mesh for separate coarse and fine treatment. The plus 14 mesh fraction does not require concentration. Coarse treatment includes agglomerate spiralling, belt flotation, thickening, scrubbing with sulfuric acid, de-oiling for reagent removal, and cationic flotation of fine quartz. A recent trend is to screen at coarser than 35 mesh size and eliminate coarse particle treatment, sacrificing some grade of this product. Techniques for flotation concentration of the fine size fraction are discussed.

Jan 1, 1976

By Herbert D. Drechsler

Mining Finance is the interrelated aspects of "determining the total amount of funds to employ in a mining firm; allocating these funds efficiently to various assets; and, obtaining the best mix of financing in relation to the overall valuation of the firm." The first section is an overview of the financing problem through examination and discussion of the Balance Sheet and Income Statement. The next section is a discussion of the nature of the criteria developed in feasibility study. The third section describes type of capital funds, and the final section describes case studies of mining finance

Jan 1, 1985

By W. J. Rooney, James Fisher, W. O. Hotchkiss

During the summer of 1927, the Department of Terrestrial Magnetism of the Carnegie Institution of Washington joined with the Michigan College of Mining and Technology in conducting a series of earth-resistivity measurements in the Michigan copper country. The geological structure in this section is quite varied and fairly well known. The purpose of the investigation was to discover the correlation between the variations in electrical resistivity of large masses of soil and rock in place and the geological structure below the surface. The work done may be roughly divided into two parts: (1) Measurement and study of the variations in resistivity with depth, or with volume, to establish such general relations as exist between the two; and (2) the determination of the specific resistivity of various formations in order to make available more fundamental data which may aid in the interpretation of the results of the former type of measurement. A report by Mr. Rooney, which gives in detail the measurements made and the results obtained, forms the basis for this article. Measurement and Study of Variations in Resistivity The possibility of applying data from measurements of the physical properties of earth material to the study of the geological structure has long been recognized, and a number of methods for determining the position and character of concealed rock strata by means of seismic, gravitation, magnetic and electrical measurements made on the surface are being used with varying degrees of success. One physical property which varies widely for different materials, and hence affords an opportunity for distinguishing between them, is their electrical resistance. Locations • were selected where the geological structures were well known and where the depths to the water level and bed rock had been determined by drilling. The problem was to determine the value of measurements of resistivity and its variations as indications of the geological structure below the surface.

Jan 1, 1929

Jan 7, 1976

By A. J. Lynch, J. A. Holmes, F. C. Bond, D. W. Fuerstenau

This is an outstanding paper on comminution theory and represents a considerable advance in mathematical formulation. It clears the way for a discussion that should ultimately decide whether the work index should be considered as a parameter according to the Third Theory or as a constant. In the empirical differential equation dE = C dx/xn either C or n must be treated as a variable to satisfy known crushing and grinding conditions. The author has chosen the exponent n as the variable, with C as a constant.

Jan 4, 1958

By S. K. Kawatra

In order to take full advantage of the use of manipulatable variables to effectively control the response of coal flotation circuits to disturbances and to optimize circuit performance, the effects of each manipulatable variable must be understood with respect to the mechanisms responsible for particle recovery. This paper pays particular attention to the critical role of the froth phase and its effect on circuit behavior and control and emphasizes that in order to optimize the separation of coal from gangue by flotation it is necessary to consider particle behavior in both the pulp and in the froth while developing a control strategy. Data obtained from the extensive sampling of the flotation circuits in two coal preparation plants are used to illustrate this concept; by showing first the effects of reagent addition levels on the mechanisms responsible for particle recovery and second how this information can be used for control strategy development.

Jan 1, 1984