Search Documents

By J. R. Thoenen

IN five years mineral wool has grown to a thirty-million-dollar industry from one whose output was valued, in 1933, at $1,700,000. Ten years ago, in 1928, there were only seven producing companies, with an annual output of but 50,000 tons. By 1936 fifty or more companies were producing half a million tons. The industry is still growing vigorously and will profit from the expected activity in building in 1339, for two-thirds of this material is used for building insulation and to assist in fire-retarding, in both new and old homes. It is as useful in the South, to protect against heat, as in the North, to keep out the cold, if one may speak nontechnically. It is a concomitant of air conditioning, that new addition to the American standard of living that began in theatres, department stores, and railroad dining cars, and is rapidly progressing down to small homes. Here, then, is an industry that is only beginning to have a present, and one with an almost certain important future; one that depends upon mining and the by-products of mining for all of its raw materials; one that every progressive mining man should know something about.

Jan 1, 1939

By Royal Preston Jarvis

minerals of different specific gravities. It is simple in construction, easily operated, capable of treating large quantities in a short time, and highly efficient under various conditions. The question, whether the material to be jigged has first been sized, determines the two principal methods of jigging. Jigging preceded by close sizing, generally known as the Continental or German system, involves a more or less elaborate series of screens or trommels, with attendant cost for installation, operation, and repairs. Jigging without sizing, known as the English system, is, according to Munroe,1 a development of the hand-jigging formerly employed in Cornwall . and introduced by English miners to this country." In its simplest form, the method consists in jigging an ore-mixture previously crushed to some maximum size (although, in some cases, even this preliminary is omitted) oil a relatively coarse sieve, and then jigging again on a filler sieve, the material passing through the first sieve and bedding. While many modifications have been necessary to adapt it for use in mills of large capacity, where hand-work was necessarily, replaced by machines, the principle remains the same; the fact that the English system has been successfully employed, both in this country and abroad, is well known; and arguments have been made for its efficiency and applicability in a wider sphere than it has occupied hitherto. II. REVIEW OF PREVIOUS INVESTIGATIONS. The fact that treating a mixture of minerals under jigging conditions increased the amount of mineral saved, or, as Professor Richards aptly terms it, 1 ?the extra jig-catch," has long been known. To account for this fact a number of theories have been proposed. The work of Rittinger2 in this field has, for many years, been a classic in the literature of ore-dressing. For the purposes of my present paper, however, the work of two American investigators, Prof. H. S. Munroe and Prof. R. H. Richards, is chiefly concerned. Professor Munroe has given the results of an elaborate series of experiments,3 and his deductions, based largely oil theoretical grounds, of this work. After reviewing briefly the two systems of jigging, followed by a discussion of Rittinger's formulas and

Sep 1, 1908

By J. E. Campbell, A. W. Wesner, M. Pobereskin

This paper summarizes the results of an investigation sponsored by The Coates Steel Products Company. The objective was to determine the relative effects of certain chemical and physical properties on the wear resistance of grinding balls when grinding cement. In making this study, a number of types of balls were used in both dry and wet grinding in commercial ball mills. The radioactive-tracer technique was used in separating the test balls from the rest of the mill charge and in sorting the different types of halls that were all tested at the same time for each of the grinding operations. PROCESSING OF GRINDING BALLS In order to determine whether the properties of grinding balls, namely, composition, microstructure and hardness, can be related to the rate of wear, the halls used in this study were selected to represent various combinations of these properties. It was recognized that the mechanism of wear was not the same in the wet mill as in the dry mill. Therefore, the types of balls tested in each of the two environments were not necessarily the same. However, all of the types of balls evaluated in the dry mill were tested simultaneously for one time period, while those evaluated in the wet mill were tested simultaneously for three different time periods. All of the test balls were separated from the charge when the mill was dumped. All of the balls were of 0.940-inch diameter when charged, and all but the regular production balls were finish ground to this size to eliminate the decarburized surface layers. The steels and processing methods used, as well as the micro-structures and hardness levels of the balls, are described as follows: Regular production forged SAE 1095 steel balls were used in both the wet and dry mills. They were forged to a nominal diameter of 0.940 inch and quenched in oil from the forging temperature. Each retained a partially decarburized surface layer from the forging bar stock; the maximum depth of this layer was about 0.030 inch and the decarburization was negligible where the ball was sheared from the bar. The hardness at the surface was 40 to 46 Rock-well C in the partially decarburized area and 57 to 62 Rockwell C in the areas not decarburized. The hardened zone extended to a depth of about one-third of the radius. Below the decarburized layer, the hardened zone consisted primarily of hard as-quenched martensite with varying amounts of retained austenite. This structure changed to fine pearlite at a depth of about one-third of the radius. In order to eliminate the effect of the decarburized layer, a set of production balls of SAE 1095 steel was forged to about a 1-inch diameter, quenched in oil from the forging temperature, and ground on ball-bearing grinding equipment to a 0.940-inch diameter to remove the decarburized layer. The balls' hardened zones were similar to those in the previous set. The hardness of the finished surfaces was 52 to 60 Rockwell C. A slight amount of decarburization apparently remained after the removal of about 0.030 inch from the surface. Balls of this type were tested in the dry mill only. Another set of forged SAE 1095 steel balls of 1-inch diameter was heated to 1500 F and quenched

Jan 1, 1961

G. A. Moore—The tin-fusion method has been a very favorable possibility for many years. The authors apparently have settled the question that delayed the method for a long time by showing that no hydrogen is absorbed in the tin. This, of course, is very important. I want to make a few remarks concerning the absolute accuracy of analysis, which must be the final basis for deciding among the various methods. From the figures in the paper, there seems to be some re-maining slight discrepancy on the actual amount of hydrogen present in various samples which may be presumed essentially identical. (This is of the order of the precision of individual analyses but appears in averaged results.) From the analyst's viewpoint, the tally of hydrogen content can be regarded as occurring in three portions. First is a large portion which comes off easily and automatically during sample storage and later on heating in the apparatus. This is fairly easily analyzed. Second is an item which may be either positive or negative in the tally sheet. In warm or hot evolution, this is a portion which, in practice, can never be re-

Jan 1, 1951

By H. J. de Haan, J. van Lookeren

In view of their size and favorable characteristics, Shell's heavy-oil fields on the eastern coast of Lake Maracaibo, Venezuela — known as the "Bolivar Coast" — are obvious candidates for the application of thermal recovery methods. During the last decade various methods have been tested, such as steam drive,', steam soak and in-situ combustion.3 Steam soak was discovered as a promising production method rather accidentally in 1969, during early steam drive testing in the Mene Grande Tar Sands1 When steam erupted at the surface due to breakdown of the overburden, the injection wells were back-flowed to relieve the reservoir pressure. This resulted in high oil production rates, all the more impressive because the reservoir is unproducible by primary means. It was concluded that injection of limited amounts of steam might be a very effective method for stimulation of heavy-oil wells. To obtain information that would be more widely applicable, testing of the process was continued in the eastern part of the Tia Juana field (Fig. 1). Here even more favorable results were obtained than in Mene Grande. This created sufficient confidence to prompt a large-scale project, which was considered essential for an adequate evaluation of ultimate recovery, steam requirements, mechanical problems and economic prospects. To obtain an early answer on the ultimate recovery a fairly depleted area was selected in the western part of the same field ("A" in Fig. 1). The first steam was injected in March, 1964. This paper describes the performance until the end of 1966. The production mechanism and well inflow performance are discussed in some detail. In view of the favorable results obtained so far, steam soak operations have expanded considerably since the start of this project. Presently, five other projects are under way, of which two are about the same size as the one under discussion, with further extensions being programmed. Description of the Project Reservoir Data Shell's part of the Main Tia Juana reservoir has a proven area of 8,800 acres and an average net oil sand thickness of 130 ft. It contained an initial quantity of 2,750 million bbl of stock tank oil (STOIIP), with an API gravity ranging from 10 to 15 API and a viscosity of 100 to 10,000 cp (at 122F). As a geological unit it is known locally as the Lower Lagun-illas member of the Lagunillas formation, which is early Miocene in age. The sand bodies are believed to be distributary channel sands deposited in a lower coastal plain. Most of the channel sands have lateral and some vertical communication. The field was developed mainly in the period from 1936 to 1950. The ultimate primary recovery is estimated at 18.1 percent of STOIIP, of which 12.5 percent STOIIP had been produced by the end of 1963 from some 540 wells. By then the average pressure had decreased from an initial value of 960 to 550

Jan 1, 1970

By AIME AIME

The first session, held Tuesday evening, February 23, in North Sheffield Hall, was called to order by Louis V. Pirsson, Chairman of the Local Committee, who introduced Prof. Russell H. Chittenden, Dean of the Sheffield Scientific School of Yale University. Professor Chittenden, in behalf of the Governing Board, felicitated the Institute on its visit to New Haven, and cordially welcomed the members and guests to the University and the city. Dr. James Douglas, who presided at the meeting, responded in behalf of the Institute. The Secretary announced that, upon the proposal of many members, the unanimous report of the Committee on Membership, and .the unanimous recommendation of the Council, the following members had been unanimously elected by the Board of Directors Honorary Members in the American Institute of Mining Engineers Prof. Richard Beck, of Freiberg, Saxony, in recognition of his distinguished service to technical literature, and the cordial

Apr 1, 1909

By D. F. Hewett

CONTENTS PAGE Introduction 1 Geologic features of eastern Oregon 2 Geology of the Sumpter quadrangle 2 Rocks older than the ore deposits 3 Rocks younger than the ore deposits 8 Lodes of the Sumpter quadrangle 8 Areal distribution 8 Geologic distribution 9 Major features of the veins 9 Mineralogy and texture of the veins 13 Ore deposits zonally disposed around the Bald Mountain batholith . . . . 13 Summary of mineralogy and texture 32 Zonal relations 33 Ore deposits zonally disposed around Greenhorn Mountain batholith . . . 36 Zonal relations 37 Relation of textural features to zonal arrangement of veins 37 Summary of zonal relations 38 Comparison with similar districts 39 Outlook for the district 40 INTRODUCTION IN an earlier report on the Sumpter quadrangle1 it was briefly stated that the quartz lodes of that region might be separated into several groups or belts on the basis of the kind and abundance of the minerals of which they are composed, and that these belts were disposed as areal zones around the principal intrusive mass of the region. When the opportunity to revisit the region was offered in 1929, as a result of a cooperative agreement between the State Mining Board of Oregon and the United States Geological Survey, it seemed advisable to pay particular attention to this feature of the lodes, in the hope that if the idea of zonal relations was confirmed it might serve as a guide in exploitation.

Jan 1, 1931

By A. Thielen

In experiments for the production of steel the principal problem has always been the introduction into, or removal from, the iron of a definite quantity of carbon. Although the solution of this problem had engaged a more or less blindly and empirically directed effort for a long time, it was only with the development of analytical chemistry that the rôle which carbon plays in the constitution of steel was disclosed in its full significance, and that many of the problems confronting the steel-maker were thereby more clearly defined than before. For a long time, and to a certain extent even to this day, the percentage of carbon in steel has been the controlling means of deter mining its quality and hardness. In many cases the percentage of carbon alone has been relied on for judging large consignments, such as the large deliveries of wire-billets and blooms to America during the past twenty years; and though to-day the influences of the other constituents are recognized and many other considerations are taken into account, and though, moreover, some special steels, such as the Hadfield manganese steel, apparently dispense to a certain extent with the assistance of the carbon, yet fix our Bessemer, Thomas, Siemens and crucible steel the carbon still remains one of the most important constituents, and I venture to say it is indispensable. In order to produce in the Bessemer converter a steel of a certain required percentage of carbon, two methods, as is well known, present themselves. By the one the decarburization process is stopped when the desired carbon limit in the bath has been reached ; by the other the bath is completely decarburizecl, and then a calculated amount of carbon added in the form of spiegel, ferro manganese, etc. In Germany the latter method only was adopted, and it was retained when the Thomas-Gilchrist process for the production of low-Phosphorus steel from high-phosphorus iron eame into use, since from the nature of the new process complete decarburization is neces-

Jan 1, 1891

By F. R. Hensel

P. R. Kalischer.*—I should like to amplify a little one of the points made by Dr. Hensel, and rather violently disagree with him at the same time. He brought out the point that when the higher forming pressures are used on the green compacts there is a marked decrease in the density as sintered. We found that to be true and, of course, many of you notice that that is true with copper compacts also. But, in my opinion at least, it is not true that the expansion is due to entrapped air. We have vacuum-pressed both silver and copper compacts and obtained almost exactly the same numerical expansion as we secured by pressing in air. The powder, however, that is vacuum-annealed does show a slight decrease in expansion on sintering, but almost the entire increase on expansion can be overcome by very slow rates of heating. And it is our opinion that a majority of the expansion is due to dissolved oxygen in the discrete metal particles themselves rather than to entrapped gases. Another interesting observation that we have made is that often with silver or copper compacts it is desirable to silver solder or braze the compact into some part of a piece of equipment after completing powder metallurgical operations on it. If such a compact is sintered and coined, say a silver compact, given an initial forming pressure of 10 to 15 tons per square inch, and sintered, there is an adequate amount of shrinkage and it can be coined at about 50 or 60 tons per square inch and bring up the density nearly to theoretical. If, then, that compact is silver-soldered into some part of a fixture or a machine, it will expand very beautifully, and the only way that this can be overcome. as far as we know, has been to reanneal after the coining operation at a temperature higher than is to be used in any subsequent operation. In that way, a density very nearly theoretical can be achieved, but the coining operation cannot be carried to the excessively high pressures or expansion and bubbling of the compact will occur again.

Jan 1, 1945

By H. Foster Bain

THERE has never been a great civilized nation which did not have a mining industry; civilization cannot flourish without metal mining. Without tools we can have none of the 'industries that are the foundation of civilization and without metal mining we cannot produce the material of which tools are made. Therefore, if we have no metal mining we have no metals, no tools, no civilization. An example to illustrate this may be drawn from a recent article in the Saturday Evening Post which described the run-down condition of modern Athens. Athens is nothing but a busted mining camp! In its palmy days the Greeks so applied the leasing system to the silver mines of Laurium that the royalties, paid the expenses of government and instead of a tax bill the inhabitants received a pay check. The Persians came over to capture these mines but the Greek navy was built to defend them. When the silver mines played out, Greek civilization declined.. Our mining must continue if our civilization is to continue.

Jan 1, 1921

By Scott Turner

GOLD AND SILVER, the monetary metals, have presented in the last year a striking contrast; gold has experienced unusual prosperity, while silver has been depressed more severely than ever before. Gold mining has been hailed as the only basic industry that is able to thrive on depression; the new gold produced is thought by many to be the most important material for the reconstruction of prosperity. Silver production, meanwhile, has been sinking to its level of 40 years ago, and its price to a level never before recorded. These factors have reduced the value of silver produced in 1932 to about the value of the average annual production more than a century ago, that of the decade 1801-1810. No other major commodity in world trade appears to have suffered a greater decline during the present depression.

Jan 1, 1933

By L. E. Fish, G. S. Wyman

CHUQUICAMATA open-pit mine is capable of producing a total of 105,000 tons daily. When the sulphide plant is operating to capacity the distribution of this quantity will be approximately 30,000 tons sulphide ore, 30,000 tons oxide ore and 45,000 tons of waste. At that time the combined capacity of the oxide and sulphide plants will be about 540 million lb of copper per year. Twenty one benches have been opened to date and all are still active except the three top ones at the northeastern limit of the pit. These have been pushed back to final slope line. The pit is 8850 ft long, 3540 ft wide and 980 ft deep. Benches are not all developed to a standard height as the large development shovels used in cutting new benches have been of different size and range. At this time new benches 521 ft high are being developed with an' 11-yd shovel. Ore haulage through the greater part of the pit operation has been on down grades to the crushing plant. With the opening of bench F-4 in April 1944 the first adverse-grade ore haul was encountered. Of the total tonnage now being mined, 35 pct comes from the four benches that are below the level of the crushing plant yard. Waste had been dumped on the same or nearly the same level as the bench from which it was removed up to the opening of bench F-4. Waste from this and lower levels is hauled to the level of the crusher, yard where it must cross the flow of ore traffic to reach the only available dumping space to the east of the mine. The average ore haul is 3.13 miles one way shovel to crusher, and the average waste haul from that portion handled by railroad is 3.32 miles one way from shovel to waste dump. Waste that is being removed by truck haulage from the upper part of the -mine is hauled an average of 1 mile. Ore loaded by trucks is hauled 3/4 mile to a car loading ramp and then by rail to the crushing plant. Drilling and Blasting There are two types of development for blasting being used: One for opening new benches and the other for bank shooting. The former consists of 9a in. diam churn-drill holes drilled 11.8 ft center to center in rows 10.2 ft apart with the holes staggered in the rows thus giving an equilateral-triangle pattern of 11.8 ft on a side. After the first block, 492 ft long by 71.5 ft wide, is shot in the pattern described above, the cut is advanced by smaller shots consisting of four rows of holes spaced 23 ft center to center with the rows 23 ft apart. These shots are fired in conjunction with side shots in which the holes are drilled 33 ft center to center and 29.5 ft back from the toe, thus squaring up the bank for subsequent shooting. An average bank shot consists of about 60 holes drilled in two rows parallel to the face, 30 holes to

Jan 1, 1952

By H. A. Domian, H. Biloni, G. F. Bolling

Jan 1, 1965

By R. J. Watson, A. H. Juch

About half a million sucker-rod pumps are installed in oil wells in the U. S. alone. In Venezuela, too, the system is widely used; some 5,000, or 90 percent, of Cia. Shell de Venezuela's wells produce a total of 400,000 BOPD by this method. Most of the crude pumped is viscous, gassy and contains relatively small amounts of free water. API gravities vary from 90 to 16O; dead oil viscosities vary from 10 to 10,000 cp at the pump; and GOR's range from 100 to 2,000 cu ft/bbl. Pumps are set at depths ranging from a few hundred to 6,000 ft; the average setting depth is about 2,500 ft. From the literature, it appears that although recent years have seen significant progress toward understanding the rod pumping system as a whole, relatively little attention has been paid to those key items, the sucker-rod pump and the subsurface gas separator or gas anchor. Perhaps because of proration in the U. S., pump manufacturers have seemingly concerned themselves more with the durability of their product, achieved mainly through robust design and metallurgical know-how, than with its working efficiency. In 1963, CSV commenced a major rehabilitation and expansion of its heavy oil fields along the Bolivar Coast. The advent of the more efficient gravel-packed completion and of large-scale thermal recovery (mainly steam soak) operations resulted in well potentials *Now with B. I. P. M., The Hague, The Netherlands. greater than pump capacities. Hence, an urgent need arose to improve over-all pump efficiencies and to attack those special problems related to the production of both the extremely viscous and the hot, steam-laden crudes that formed an increasing proportion of the total stream. There followed a detailed investigation and testing program, carried out in close cooperation with a major pump manufacturer. This culminated in the introduction to the oil industry of a new line of sucker-rod pumps. Early Investigations and Experiments Field Tests Extensive field tests were carried out in three primary Bolivar Coast wells with an in-situ dead oil viscosity ranging from 400 to 6,000 cp. In these installations provision was made to (1) monitor bottom-hole pressures below, in and above the pump by means of pressure transducers, and record casing- and tubing-head pressures continuously; (2) measure accurately the annulus gas, as well as measure the tubing gas and liquid production from the well; (3) take special PVT samples of the well fluid; (4) measure power consumption of the prime mover; and (5) measure the rod loads at the polished rod. A typical test installation is illustrated in Fig. 1. It was established from the pressure transducers that with viscous oils, there is considerable flow resistance across the pump and gas anchor assembly. Pressure surges were observed over each pump cycle,

Jan 1, 1970

By A. B. Parsons

AT the outset, the authors of this paper desire to file a disclaimer and an, explanation. They have no inside information from occult sources; neither of them feigns clairvoyant powers in the slightest degree. It is true that they have indicated on be graphs an approximate trend for the consumption of seven important mineral commodities up to the year 1954. At best this is a risky business; the figures do not pretend to be any- thing more than reasoned conjectures that are predicated on an attempt to evaluate some of the more obvious of the many factors that are likely to have a bearing on the future.

Jan 1, 1937

By H. T. Kennedy, S. M. Avasthi

An equation developed for gaseous hydrocarbon mixtures predicts molal volumes with an average absolute deviation of 0.73 percent when applied to 264 natural gas and condensate systems including 2,043 PVT points. Another equation developed for liquid hydrocarbon mixtures predicts molal volumes with an average absolute deviation of 1.12 percent when applied to 346 crude oil systems including 1,759 PVT points. Both equations require composition of the mixture to be expressed as mole fraction of methane through heptanes-plus, hydrogen sulfide, nitrogen and carbon dioxide, together with the characteristics of the heptanes-plus fraction in addition to the temperature and pressure. The equations cover wide ranges of the variables involved, and their accuracy is considerably better than that of other available methods. The equations were differentiated to allow calculation of the coefficients of isothermal compressibility and isobaric thermal expansion. (In this paper the coefficient of isothermal com-pressibility and the coefficient of isobaric thermal expansion will be expressed as compressibility and thermal expansion coefficient, respectively.) Equations to calculate these quantities are presented. INTRODUCTION Calculations of reservoir performance for petroleum reservoirs require accurate knowledge of the volumetric behavior of hydrocarbon mixtures, both liquid and gaseous. Compressibilities are required in transient fluid flow problems, and thermal expansion coefficients are important in thermal methods of production. An accurate laboratory investigation of the PVT behavior of each reservoir fluid encountered would be costly and time consuming. For this reason various correlations for predicting fluid properties have been developed and recorded in recent literature. Correlations have been presented in the form of graphs, tables and equations. Since an increasing number of studies are being conducted with the aid of electronic computers, recent efforts have been directed toward development of correla-tions suitable for computer programming. Application of computers permits the use of more complex correlations which otherwise are not feasible. Moreover, methods for predicting reservoir performance, particularly those based on the compositional material balance, depend upon the capability of accurately expressing the molal volumes and other fluid properties as functions of pressure, temperature and composition. The coefficient of isothermal compressibility c is defined by

Jan 1, 1969

By J. W. Givens, P. B. Crawford

A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. INTRODUCTION One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of water-flooding or gas cycling programs.1-5 However, there arc few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures.6,7 It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee8 it has been widely used to study numerous types of fluid displacement problems. The potentio- metric model can be used for fluid displacement studies when the following assumptions are valid: (a) steady-state conditions exist; (b) the mobilicy ratio is one; and (c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN — ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattem with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattem expressed as a per cent. The cross-hatched areas of this

Jan 1, 1967

By C. A. Allen

For over three years we have been endeavoring to reduce the number of fatalitics and minor accidents in Utah. The physical condition of the FIG: 1.—Number kiLlEd per million short tons of coal produced in ColoraI)o, New Mexico, utah, Wyoming, and bituminous mines of the United States 1014 to 1920. mines, concentrators, and smelters is good, yet the number of accidents,

Jan 1, 1923

By C. A. Allen

For over three years we have been endeavoring to reduce the number of fatalitics and minor accidents in Utah. The physical condition of the FIG: 1.—Number kiLlEd per million short tons of coal produced in ColoraI)o, New Mexico, utah, Wyoming, and bituminous mines of the United States 1014 to 1920. mines, concentrators, and smelters is good, yet the number of accidents,

Jan 1, 1923

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969