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By H. H. Rachford, and J. D. Rice

The effectiveness of digital computing machines in making technical calculations depends on how well the work is arranged to utilize the capability of the machines. This note presents a particularly useful way of calculating hydrocarbon vapor-li.quid equilibrium in the flash vaporization (or condensation) system. The method is well suited to sequence-controlled computing equipment. It is not limited to equilibrium calculations and may be used for solution of most implicit equations in one variable. INTRODUCTION There is increasing interest in the use of electronic digital computers in research and engineering calculations. This is a fortunate and inevitable trend in view of both the increasingly extensive numerical work which is becoming a routine part of many daily production operations and growing demand for the overwhelming amounts of calculations required by newly developed numerical methods for solving heretofore unsolved problems. Machines are in many ways ideally suited to the task but of necessity present certain difficulties. for a particular poblem to be solved must often be formulated quite differently from the way it would be arranged for manual solution. This is done in order to take advantage of the inherent speed and precision of electronic computers and at the same time to limit the need for number storage to the capacity of the machine. Therefore, this note is submitted to present a general and quite powerful method of finding solutions of the frequently encountered implicit equation: F(x,y1,y2,...ya)=0.......(1) where the root, x, is to be found for a given set of y1, ... yn.. The procedure is well suited for use with computing machines, for it usually requires but little storage or programming beyond that necessary to evaluate F. HYDROCARBON EQUILIBRIUM The method is described in terms of the problem it was designed to solve, i.e., the calculation of hydrocarbon vapor-liquid equilibrium in flash vaporization. Given the composition of a hydrocarbon mixture and appropriate values of the equilibrium ratios K, to find the phase ratio and compositions in a closed system: let z, be the mol fraction of the i-th component in the mixture. If K, is the ratio yl/xl, where y, and x,

Jan 1, 1952

By Arthur Zentner

THE essentials of the electrolytic zinc process, as now used in commercial plants, date back to work done by Letrange in 1881. He used sulfuric acid to leach roasted sulfide and ,oxide ores, purified his solution very much as we do now, and electrolyzed the purified zinc sulfate solution. Ten years later Hoepfner developed a process using chloride solutions, and built three plants. One in England operated until 1924 in one of the works now merged in the Imperial Chemical , Industries, Ltd. Ashcroft built a plant in 1898 in the Broken Hill district of Australia. He used both chloride and sulfate solutions.. While his work failed, the aid his published results have been to later workers has made him an outstanding contributor to the de- velopment of the electrolytic zinc process. A good deal of work was done in the following years, aiming to electrolyze zinc chloride solutions and fused zinc chloride. Quite a bit of work on sulfate solutions was also done in the last years before the war. With the outbreak of the war, metal demand and rise in metal prices provided the stimulus which resulted in the remarkably rapid commercial development of electrolytic zinc. In this last period of development, all the work brought to commercial fruition has been with sulfate solutions. The high-density process, or the Tainton process, is used, as you know, in the Sullivan electrolytic zinc plant at Kellogg, Idaho, and will be used in the Evans- Wallower plant now being built at East St. Louis. The low-density process is used by the other plants now operating in the United States and other countries. There are now in operation and under construction four electrolytic zinc plants in the United States, two in Canada, two in Italy and one each in Australia, Rhodesia, Poland, Norway and Germany.

Jan 1, 1929

By John J. Collins

The plight of the Japanese mining business is pitiful. Coal mines were given the highest priority for all materials they needed, yet between the end of the war and June 1948, the government was obliged to subsidize them to the extent of 22 billion yen, this being the difference between the consumer's price and the producer's price. Most of the metal mining companies have been operating at only one fifth to one third of war-time production rates, and financial losses have been terrific. The chief difficulties have been a plethora of office workers and a dearth of equipment, supplies, and miners. The principal material needs at metal mines are steel rails. cars, plates, nails, rubber hoses, and belting, to say nothing of modern core drills which are totally lacking. Until recently the great shortage was in coal; for lack of fuel the smelters and factories failed to produce the very metals and equipment now needed to operate the mines. Nation-wide shortages have created a monstrous inflation of prices throughout all the economy, currently amounting to 200 times the prewar figures. For example, the price of copper ranged from 500 to 900 yen per metric ton for many years until 1937, but in mid-1948 producers were

Jan 1, 1949

By R. G. Knickerbocker

A STURDY and consistent expansion of the metal industry occurred in 1947 exemplified by an increase of approximately 30 per cent in steel consumption over 1946. For this major reason, ferroalloy metals have seen their most useful and important peace-time year. The current domestic rate of consumption of high-grade ferroalloy ores, together with added consumption of new foreign producers as well as for eign nationals' restrictions on high-grade exports, makes very evident the increasing difficulties of obtaining sufficient high-grade ores. This accentuates the need for new and less expensive methods of production of ferro-alloy metals of higher purity from lower-grade domestic resources. As an important factor in preparedness, procurement of these high-grade, -critical ferroalloy minerals and metals for our nation's stock piles is a most important task. Also, this stock-piling can be the means of supplying incentive for the industrial development of the new metallurgical processes and plants necessary for the recovery of ferroalloy metals from our domestic low-grade deposits.

Jan 1, 1948

A. H. Bromly, Zihuatanejo, Guerrero, Mexico (communication to the Secretary*):—The following criticism of what "is offered as a summary which may be found useful by mining engineers," is not dictated by any captious spirit, but in the intereet of historical and scientific accuracy. The States of Queretaro and Oaxaca have produced sufficient silver to warrant more extended notice. Referring to Pachuca, State of Hidalgo, the eomewhat loose and inexact statement is made that "the ore-depdsit is an andesite, intermixed with quartz-veins, rich from the surface." A better description mould be,—the ore-deposits consist of quartz-veins in andesite. It is notable that many of the rich shoots worked in recent days did not come to surface. In consequence, Pachuca is often quoted by the ill-informed as a camp in which values improve with depth, the truth being that the veins carry shoots, or clavos, some of which were exposed at surface and some not. The name of " electric plow," applied to the mechanical stirrer of recent use, is certainly not to be recommended. The stirrer, or agitator, consists essentially of a traversing gang-plow, operated by power through shafting; drums, and wire-rope. The fact that in certain plants the motive-power used is electricity does not make it an electric plow. Such a name suggests a machine of which the motor is an essential and integral part; which is not so in this case. A lathe in a factory driven by water-power is not called a hydraulic lathe. My experience agrees with Dr. Raymond's note as to azulapue, which in some districts is also applied to blue copper carbonate. The El Oro, Esperanza, and Mexico mines should be allocated to the State of Mexico; the Dos Estrellas being in Michoacan, as stated. The El Oro quartz certainly does not appeal to me

Jan 1, 1910

By T. G. Lovering

Nonparametric statistical tests have practical application to many geological problems because, unlike the standard statistical tests, they do not require assumptions regarding the form of the population frequency distribution. Many of them do not even require that the variable be susceptible to numerical measurement. These tests are useful either 1) for geological data representing population distributions of unknown form, or otherwise not meeting the requirements for standard parametric tests; or 2) for sample attributes that cannot be measured but only ranked in order of relative magnitude. The application of two such tests will be illustrated. The Kolmogorov-Smimov test will be used to test for significant differences in copper distribution in samples of two rock types; the Spearman rank-correlation method will be used to determine whether there is a significant association between intensity of rock alteration and copper content of the rock. Nonparametric tests are, in general, quicker and easier to perform than the corresponding parametric tests, and they may be applied to a greater variety of data. They are not as powerful as the standard tests if used on data to which the latter are applicable, and computer programs utilizing them are not generally available. The use of standard or parametric statistical procedures for the interpretation of measured geological data is familiar to most mining engineers and explora- tion geologists. The computation of product moment correlation coefficients on sample assays for more-than one component is already standard procedure in some company operations, as is the use of Student's F test and Snedecor's F test for the comparison of means and variances of sample groups. The application of these three tests is limited by the prerequisites that the samples must be random, independent representatives of normally distributed populations and that the variables involved must be measurable. If such tests are applied to data which fall short of fulfilling these prerequisites, then the probability level attributed to the computed statistic is invalid and the conclusions based thereon may be erroneous. A number of nonparametric, or distribution free, statistical tests have been developed for use with data which are not amenable to standard parametric procedures. These tests have been widely used in the behavioral sciences such as psychology and sociology for some time, but their application to geologic problems is relatively new. Nonparametric tests may be grouped into two main categories: those which test for significant differences in a single variable by comparing either sample values with a standard value or representative values between two or more groups of samples; and those which test for significant association between pairs of variables in a single group of samples. The versatile chi square test, the Kolmogorov-Smirnov one and two sample tests, the Wilcox matched pairs signed ranks test, the median test, the Mann-Whitney U test and the Cochran Q test are examples of nonparametric tests with demonstrated or potential geological applications that belong in the first category. The contingency coefficient, Spearman rank correlation coefficient, Kendall rank correlation coefficient and the

Jan 1, 1963

By Herman Poole

WHEN finely divided ferrous sulphide, FeS, is roasted at a moderate, carefully regulated temperature, the iron and sulphur are oxidized, the first products being probably ferrous oxide and sulphurous acid. In the presence of oxygen of the air the ferrous oxide soon becomes ferric oxide and in the presence of oxygen and the ferric oxide the sulphurous acid oxidizes to sulphuric acid. These facts are well known, having been established by Plattner many years ago. As a further reaction, some of the sulphuric acid parts with a portion of its oxygen to oxidize more ferrous oxide to ferric oxide, and a portion of it escapes uncombined or else unites with the iron oxides to form sulphates. Ferrous sulphate is usually soon oxidized to ferric sulphate and if the heat becomes sufficient this is then decomposed into sulphuric acid and ferric oxide. As a result of these reactions a mass of more or less pure ferric oxide is formed which is generally made porous by the escaping gases and, if rabbled properly, practically all the sulphur is expelled. If ferric sulphide or ordinary pyrites, FeS2, is roasted, a portion of the sulphur sublimes and usually burns to form sulphurous or sulphuric acid, although at times and under favorable conditions some of the sulphur is driven off uncombined and can be collected as such. Under ordinary methods of roasting, however, only a small portion escapes combustion. By the combustion of the sulphur an increase of heat is de¬veloped and, as a consequence, the reactions mentioned take place more rapidly and actively-more sulphuric acid is formed and the oxidation is more complete-nearly all the iron being left as ferric oxide with practically no sulphate or ferrous oxide. When the iron sulphide is in lumps the roasting proceeds generally as with fines, but with some changes due to mass. The

Sep 1, 1905

By G. C. Trevorrow

STRIP mining during 1943 increased considerably with further extension of mechanical loading in mines already partly mechanized; with the considerable introduction of mechanical loading into hand-loading mines; and with improvements in the use of loading equipment. Extension of the use of machinery both in strip mining and underground is due to reduction in labor supply and increased cost of labor, together with the increased demand for coal during the period of labor shortage.

Jan 1, 1944

By Robert A. Cook

Among the new devices for cheapening the cost of material entering into the manufacture of iron is the mechanical drawing of coke, by which the coke from bee-hive ovens is extracted with a minimum of manual labor. About twenty years ago, an ordinary plate-conveyer was put in use at the plant of bee-hive coke-ovens owned by the firm of Bell Bros. & Co., near Middlesboro, England. This conveyer ran close along the front of the ovens, and carried the coke to the cars. The ovens were drawn by hand, and a very great saving in cost was secured, as one man could draw and clean out twice as many ovens after the conveyer was put in use—he having no forking to do, and the coke being carried away as fast as it was drawn to the mouth of the oven. The next step was further to eliminate hand-labor as far as possible; and Mr. Thomas Smith of the Thorncliffe Iron Works, near Sheffield, patented in 1891 the machine for drawing coke which I here describe. This machine, the outcome of several years of experimenting, has now been in successful use since 1891, and there are between twenty and thirty of them in operation at present, and others building. The machine, as may be seen from Figs. 1 and 2, consists of a wedge-shaped shovel of proper width and thickness, connected with a steel rack of sufficient length to reach the back of the oven. The rack is supported by rolls, and guided by a device operated by a hand-wheel, which directs the shovel in the oven. The rack is driven by a pinion on a vertical shaft carrying a bevel-gear on the upper end. This bevel-gear is driven by another on the engine-shaft. The engine is single-cylinder, with reversible gear; and engine and machine are mounted on a truck, which is propelled

Jan 1, 1897

October Meeting of the Institute.-Invitations have been sent to the members of the following societies through the respective Secretaries to attend the October meeting of the Institute and the Dinner which will be given on the evening of Oct. 17 : American Society for Testing Materials, American Iron and Steel Institute, American Society of Mechanical Engineers, American Society. of Civil Engineers, American Institute of Electrical Engineers, . American Foundry men's Association. Members of these Societies have also been invited to contribute to the discussion of the various papers to be presented at the meeting, a revised list of which appears in the notes of the Iron and Steel Committee on p. vi. Many individuals of national and international prominence have also been invited to contribute discussions of these papers, and the response to these invitations has been extremely encouraging.

Jan 9, 1913

POSITIONS VACANT (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Metallurgist wanted for research in iron and steel. Man with experience in mills preferred. Salary $4,000. No. 13. Opening for a few technical graduates to act as instructors in mining to men at the mines under the supervision of the State mine inspector. Salary $1,800 per year. No. 14. ENGINEERS AVAILABLE (Under this heading will be published notes sent to the Secretary of the Institute by members or other persons.) Mining engineer and metallurgist open for engagement, as superintendent of mines or constructing engineer. Technically educated, with 14 years' experience in United States and Latin America in concentration, amalgamation, cyaniding, constructing. Just finished building large modern all-sliming cyanide mill in Central America. No. 18.

Jan 4, 1914

By E. P. Fleming

COMPARED to the situation abroad, the domestic industry continues to lag both as regards the production and consumption of newly mined lead. During 1938 we produced and consumed slightly over 20 per cent of the world output, whereas ten years ago the figure was nearly double this pro- portion. Labor difficulties and absence of demand were chiefly responsible for the general inactivity. In the foreign field, in spite of low metal prices, production and consumption of lead equaled or exceeded all previous records. Practically all the large companies, with the exception of those in Spain, increased operations, though it should be noted that the foreign lead mines have higher-grade ores than domestic mines. In view of the rapid expansion of the foreign industry, it is natural to expect greater progress abroad, particularly in process metallurgy.

Jan 1, 1939

By C. K. Leith, W. J. NEAD

(Glen Summit Meeting, June, 1911.) . ONE Of the most significant developments in the iron industry in recent years has been the discovery and opening of enormous reserves of low-grade ore in eastern and northeastern Cuba. The two principal fields are the Mayari and the Moa, situated on Nipe bay, in the Province of Oriente. A less well-known district of the same type is that of Baracoa, at the east of the island, and another is in Camaguey province in central Cuba. In the comprehensive estimates of the iron-ore reserves of the world, published during the summer of 1910 by the International Geological Congress in Sweden,' these Cuban deposits are estimated at about 2,000,000,000 tons. Certain it is that the reserve is a large one. The Spanish-American Iron Co., the Juragua Iron Co. (Bethlehem Steel Co.), the U. S. Steel Corporation, and others have been active in this exploration.. The Spanish-American Iron Co. has established a port for the handling of these ores at Felton, has built a railway 16 miles to the ore-fields, and has opened up deposits for steam-shovel mining. Its expenditures have reached an aggregate of about $6,000,000 in preparation for the handling of these ores. Shipment of the ore to Sparrow's Point, Md., has begun and may be expected to rise to a considerable amount in the near future. The ore reaches this point at a cost per unit of iron considerably lower than Lake Superior ores, and the presence of a low percentage of nickel gives a desirable steel. It is not the purpose of this article to consider these ores from a commercial stand-point, but rather to discuss their-origin. If our conclusions are correct, they throw light on the character of the deposits which should have some commercial significance. 1 The Iron Ore Resources of the World, an inquiry made upon the initiative of the Executive Committee of the Eleventh International Geological Congress, Stockholm, vol. ii., p. 795 (1910).

Mar 1, 1911

By C. V. Millikan, C. V. Sidwell

There is nothing more important in petroleum engineering than a definite knowledge of the pressure at the bottom of an oil well at any existing operating condition, and the relation of this pressure to the pressure within the producing formation. A knowledge of bottom-hole pressures is fundamental in determining the most efficient methods of recovery and the most efficient lifting procedure, yet there is less information about these pressures than about any other part of the general problem of producing oil. Determination of Bottom-hole Pressures Bottom-hole pressure may be calculated or determined by several methods. On an inactive well it may be calculated from the fluid head or, if the well is shut in, by adding the casinghead pressure, the static head of the gas and the fluid head. In wells flowing naturally through tubing the pressure at the bottom of the tubing may be calculated by adding the pressure at the casinghead between the tubing and the casing and the pressure due to the weight of the column of gas, but there is always possibility of error caused by fluid being in the annular space above the bottom of the tubing. If a well with tubing is flowing through either the annular space or the tubing, sufficient gas may be injected through the static space to insure that it is free of fluid but not sufficient to establish an appreciable friction loss. The pressure at the bottom of the tubing can then be calculated by adding to the pressure at the tubing head the pressure due to the weight of the column of gas. This is probably the most accurate method of calculating bottom-hole pressures. In wells flowing by gas-lift, the pressure at the point the gas enters the flow may be calculated by a gas-flow formula. Several types of pressure bombs have been used to measure the pressure at the bottom of wells. One is a piece of steel tubing with a check valve in the bottom and a connection for a pressure gage at the top. It is lowered into the well to the point at which the pressure is

Jan 1, 1931

By Albert Sauveur

IT is not without some hesitation, and even misgiving, that I venture into a discussion of the now classical Roberts-Austen Roozeboom diagram, lest I too fail, like so many other writers, in giving a satisfactory and logical explanation of these interesting curves. Roozeboom's original diagram is reproduced in Fig. 1. The generally accepted meaning of the various curves has been so often described before this Institute that it will suffice to recall it briefly before passing to my own interpretation of the changes involved.

Nov 1, 1906

By William R. Chedsey

ALTHOUGH few changes can be reported in educational methods at the mineral technology schools during 1940, other events have taken place of direct interest to, and that will have a profound effect upon, mineral industry education on the United States. In the erection of new buildings, some notable changes have been made on the campus, The U.S. Bureau of Mines Experiment Station at the University of Utah, Salt Lake City, was dedicated on May 20. The construction and equipment of this building cost between $300,000 and $400,000. It will be the general headquarters for the metallurgical division of the Bureau and will have a pronounced effect upon the mineral industries research program at the University.

Jan 1, 1941

By S. S. Arentz

An organized safety program has reduced accidents at Pioche because effort is first devoted to arousing and maintaining interest in safety, followed by training in accident prevention, assigning responsibility for the detection and removal of safety hazards, and finally, by keeping score through an adequate system of records. A health program is intergrated with the safety program.

Jan 1, 1950

By D. G. Russell

A simple method has been developed with which flowing bottom-hole pressure data from two-rate flow tests in oil or gas wells can be analyzed to estimate the formation permeability, skin factor and average reservoir pressure. The required pressure data are obtained by observation of the transient bottom-hole pressure behavior after the stabilized producing rate of the well is changed to another, higher or lower, rate. The new method yields the same information as a conventional pressure buildup analysis, but eliminates the need for closing in the well. The analysis of a two-rate flow test is of the same degree of difficulty and requires about the same engineering time for application as a conventional pressure buildup analysrs. The extended closed-in periods experienced with conventional buildups because of long, low-rate afterproduc-tion periods are eliminated by fIow tests. Other anomalous pressure buildup effects, such as "humping" due to weli-bore phase segregation, can be successfully eliminated with the new method. Generally, flow tests of about 24 hours' duration run with conventional pressure measurement equipment are sufficient for interpretation purposes. Field testing of the two-rate flow test method has established that it is a reliable and economical method which can be used in many instances to complement or even replace conventional pressure buildup methods. INTRODUCTION The principal method for estimating formation permeability and well damage, or skin factor, in a producing oil or gas well is the analysis of shut-in bottom-hole pressure buildup data.' This familiar method has been used quite successfully by reservoir engineers for many years. It is based on the solution of the radial flow equation for constant rate conditions, and requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed t + ?t bottomhole pressure vs log t + ?/?t(where At is shut-in A? time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the permeability, skin factor, and reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. Over the years several drawbacks have become apparent in the use of conventional shut-in pressure buildups for determining permeability and skin factor. The conventional pressure buildup interpretation theory assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing in to the formation. This adjustment period is commonly referred to as the "after-production" portion of the pressure buildup. In the tight reservoirs, long, low-rate after-production periods frequently occur, and the well must be shut in for several days or, in some instances, even weeks to obtain an interpretable buildup curve.' Obviously, such long shut-in times can cause loss in current income, both from reduced oil production and from the fact that personnel and pressure measurement equipment are occupied with a single well for too long a time. In other cases, even long shut-in periods do not seem to be of much aid in obtaining an interpretable buildup." If there is considerable phase redistribution (liquid fallout or bubble rise) after a well is shut in, then curves with no interpretable portion are often obtained during the buildup. In addition to instances in which wellbore effects cause trouble, there are also cases in which the major objection to use of the closed-in pressure buildup is simply the fact that the well must be shut in. When there is no proration and when the well has limited producing capacity. closing in the well means loss of income. From the foregoing discussion it is apparent that it ib desirable to have an alternative method of obtaining the same information as that derived from a conventional buildup without the need of closing in the well. One possible solution which has been offered for this problem is the use of a bottom-hole shut-in tool' which isolates the major portion of the flow string from the formation face during the buildup. In this paper an alternative method which is frequently successful in avoiding wellbore effects and which does not require the use of special equipment is presented. A new, simple method has been developed with which the flowing bottom-hole pressure data from flow tests in oil or gas wells can be used to estimate permeability, skin factor and the average reservoir pressure. The required pressure data are obtained by observation of the transient bottom-hole pressure behavior after the stabilized production rate of the well is changed to another, higher or lower rate. The need for closing in the well is eliminated, and pressure measurement periods of only 18 to 24 hours arc usually sufficient, even in tight reservoirs. Thus, the new

By S. F. Emmons

Jan 1, 1899

By Fred T. Greene

Most of the recent discussion of the mineral land law published in the Transactions is in the abstract—an exception being Mr. Goodale's paper, The Apex Law in the Drumlummon Controversyll which illustrates in concrete instances many of the practical disadvantages of what Dr. Raymond has called "The Law of the Apex." The present paper, it is hoped, may serve a similar purpose, emphasizing the necessity for a change in our mining laws, and bringing home to mining engineers some of the defects and dangers of our present code. There are many storm centers of "apex litigation" in the Rocky Mountains; and not the 1east. of them is the Wardner camp, where such litigation has been almost continuous since 1892, and the end is not yet. In their decisions, the courts have accepted the claims of the litigants that the "Wardner vein" is a broad zone varying from 250 to 500 ft. in width at the surface. This is the simplest theory which could have been advanced, and probably decreased, rather than augmented, the number of contests; in fact, every one of the claim owners seemed to feel that the greatest advantage would accrue to him if this theory were adhered to. The dominant structural feature of the Wardner vein is a persistent fault, striking N. 40' W., dipping about 40" to the southwest and called the "Wardner foot wall." Fig. 1 is a composite of two adjacent cross-sections of the vein and is a fair representation of the relative size and shape of the orebodies and their relation to the "Wardner foot wall." The country rock is a comparatively thin-bedded sericitic quartzite which has an average strike of N. 80" W. and dips at high angles to the north and south. The movement on the Wardner foot wall is apparently normal, and there has been more or less brecciation on either side of it; but as the moving mass was that above the foot wall, the brecciation has been more complete on that side, and has extended farther from the plane of movement. Many minor faults, generally of insignificant extent, resulted from the movement along the Wardner foot wall. Most of these were

Jan 1, 1916