Search Documents

By L. D. Clark

Pay-out, the ratio of capital expenditure to annual cash return can be very revealing when employed to gage the merits of a proposed mining venture. It is a quantity, numerically but not physically equal to a factor, by which cash return may be discounted to equal required investment. The fewer the pay-out years, the greater the average annual earning power of the project. Considerable material has been written in the past about the most important and difficult problem mining management faces in evaluation of a property: the optimum production rate for the venture. What daily capacity should be adopted for the proposed operation that it may be the most rewarding to those underwriting it? H.C. Hoover has said, "The most important objective is the least cost per ton mined; and minimum working costs can only be gained by the most intensive production." Theoretically and practically, the quicker the ore is removed, the more profitable should be the venture because of the saving in fixed charges, the consequent lower unit costs and the interest unearned by the profit from the unmined ore. Yet, such performance will be tempered by policy and a restraint imposed by the ratio of capital expenditure to annual cash return. * The 'Annual net profit after taxes but including depreciation and depletion allowances. former will be based upon an analysis of the economic climate anticipated, with its many ramifications including the demand for the product, prices, tax laws, the conduct of labor and related wage scales. The variables and intangibles involved in estimating the optimum production rate for a mine do not readily lend themselves to mathematical relationships or equations and the problem can become complex indeed. The more readily applicable and relatively faster appraisal method will be used which, in addition to being reasonably adequate in most cases, will serve as a guide, should a more expanded and detailed estimate be desired. The first question is what is company policy with respect to the rate of investment return? This will depend on that significant period of time referred to as the pay-out, which can be defined as the estimated interval during which capital investment is returned through application of annual cash return to its recovery. Expressed another way, it is the ratio of capital expenditure to the annual cash return. For example, if the capital investment is $C and the annual cash return is $A (after Federal tax), then $C/$A = the pay-out period in years. That is to say, if $C = $1,500,000 and $A = $214,000, then which is the mathematical expression for the period of time it takes to recover the funds originally invested in a mining enterprise. The relationship yp = $C/$A can be useful — an expression which requires only the significant tern yp to be fixed; in other words, the long range investment policy. For what is the pay-out period but an expression of that policy in terms of the speed, within practical limits, with which an individual or company may want to recover capital expenditure? A policy by which pay-out will be fixed is imperative. This ratio must lie within relatively narrow limits governed by what is economically feasible. It cannot be too low, rendering the ratio impractical or absurd, nor too great, delaying the return of capital for reinvestment beyond a commensurate interval. What pay-out will govern this policy? Federal corporate taxes would seem to present the best measure. Consider mining in Canada where new mines are exempt from Federal income tax for 3½ yr from date of first production. This exemption expressly allows The Act states: "A corporation . . . i s not required to include the profits . . . for the period of 36 months commencing with the day on which the mine came into production in reasonable commercial quantites." a company to recover capital expenditure during the early stages of production. With such an incentive, it is logical to strive for as much capital redemption as possible during this period. Thus, 3½ yr would be a major contribution to the pay-out in Canada. Furthermore, it generally takes from 1½ to 3 yr to develop

Jan 1, 1963

By T. F. McCormick

THIS year, 1950, is the golden anniversary of the construction and operation in this country of a tube mill for the sole purpose of fabricating aluminum alloy tubing. For a short period prior to the beginning of this mill, aluminum alloy tubing was obtained from foreign sources or produced in mills fabricating other metals. Indeed, it was a very short period because aluminum itself was a newcomer in the field of metals. The first sheet rolling mill had been in operation just eight years and a rod rolling mill for the production of wire and cable had been functioning one year. The first tube mill for aluminum was built by the Aluminum Co. of America in May 1900 and started production with four draw benches and five men, including the mill superintendent. The building itself was a lean-to attached to a sheet-rolling mill at New Kensington, Pa. The cost of equipment, including the draw benches, dies, mandrels, and other tools, was about $5000. This figure seems absurd in the present day but nevertheless it was questioned at that time whether or not such a large sum should be spent to embark on a new and uncertain venture. The initial production system for the new mill consisted of casting round hollow ingots in a tilting-type iron mold, reducing the ingots to bloom size outside the plant, and finally drawing to size on the draw benches. This method of producing aluminum alloy tubing survived just two years, as blooms of satisfactory quality were not obtained consistently. It was superseded by the cupping method in which a 24-in. diam circle cut from a rolled plate was formed into a tube bloom using first a small cupping press and then a push bench. It was stated that tubing so produced was limited to a maximum diameter of 2 3/4 in. and to wall thicknesses varying from 12 to 24 gage. However, for the first time all the operations were performed at one plant and the result was a quality product. Later larger cupping presses and push benches were obtained and the method continued to be the principal one for aluminum alloy tubing for almost a quarter of a century. During the interim the use of a Alan Mannesmann -type billet piercer was explored and it was used to some extent, but failed to produce consistently a smooth inside surface suitable for drawing with aluminum alloys. Experiments started during the latter stages of World War I in the production of tube blooms with a hydraulic extrusion press, led to the use of this type of equipment to make tube blooms for further drawing during a change-over period extending from 1925 until 1930. At this time the cupping method was discarded completely. From these humble beginnings, the aluminum alloy tubing business expanded until well over six million pounds were produced in a single month in the United States during World War II. The major portion of this production was in strong alloys which did not appear in the tubing picture until 1022, when 17S alloy tubing was introduced for aircraft construction.

Jan 1, 1951

By James H. Courtright, Kenyon Richard

TOQUEPALA is a porphyry copper deposit in which mineralization is localized by a large breccia pipe formed in close genetic relation to intrusive rocks. The deposit is in southern Peru, 55 airline miles north of the small city of Tacna and the same distance inland from the port of 110. Quellaveco and Cuajone, geologically similar deposits, lie 12 and 19 miles north of Toquepala. Chuquicamata is 400 miles to the south. The deposit is high on the southwestern slope about 20 miles from the crest of the Cordillera Occidental of the Andes Chain. It lies in a mountainous desert where the steep southwesterly slope of the Andes is dissected by a succession of rapidly downcutting, deep canyons. Local topography is moderately rugged with a dendritic drainage pattern and an elevation of 8000 to 14,000 ft. Volcanic peaks along the crest of the Cordillera rise over 19,000 ft. Local precipitation, including a little snow, amounts to about 10 in. during January and February, but general runoff in the region is slight. Throughout southern Peru the springs and streams are widely separated. Crude canals irrigate small farms on terraced slopes along the streams and provide sparse subsistence to the semi-nomadic inhabitants. During the past decade, engineering and geological explorations of the region, as well as the mineral deposits themselves, have required construction of a network of several hundred miles of roads. Before this, roads extended only a few miles inland. Many areas still can be reached only by trail. Toquepala was briefly described in 19th century geographical literature as a copper deposit, and it received desultory attention from Chilean prospectors early in the present century. It was first recognized as a mineralized zone of possible real importance by geologist O.C. Schmedeman during an exploration trip for Cerro de Paso Copper Corp. in 1937. The discovery was late as compared to earlier recognition of Chuquicamata, Potrerillos, and Braden of Chile and Cerro Verde of southern Peru. This was due partly to the region's difficult accessibility but principally to the obscure character of the outcrop evidence of copper. From 1938 until 1942 Cerro de Pasco Copper Corp. partially explored the deposit by adits and diamond drillholes. This campaign was supplied by a 60-mule pack train continuously shuttling over a 30-mile trail. Northern Peru Mining & Smelting Co., a wholly owned subsidiary of American Smelting & Refining Co., undertook regional engineering stud- ies in 1945 and drill exploration in 1949. According to published data1 the deposit contains 400 million tons of open pit ore averaging a little over 1 pct Cu. It is currently undergoing large-scale development by Southern Peru Copper Corp., which is owned by American Smelting & Refining, Phelps Dodge, Cerro de Pasco, and Newmont Mining. Summary of Geology: The deposit is situated in a terrane composed of Mesozoic(?) and Tertiary volcanic rocks intruded by dioritic apophyses of the Andean Batholith. These formations are exposed in a northwesterly trending belt about 15 miles wide. Along the northeast they are unconformably overlain by Plio-Pleistocene pyroclastic rocks, which occupy much of the crest of the Andes, and along the southwest they are covered by the Moquegua formation of Pliocene(?) age. The mineralized area, oblong in shape and about 2 miles long, has been a locus of intense igneous activity. Several small intrusive bodies having irregular forms occur within and adjacent to a centrally located, large breccia pipe. The mushroom-shaped orebody consists of a flat-lying enriched zone of predominant chalcocite with a stem-like extension of hypogene chalcopyrite ore in depth within and around the pipe. This breccia pipe is relatively large and has been formed by repeated episodes of brecciation. Small satellitic pipes occur at random within a 2-mile radius of this central pipe. These too were individual sourceways of mineralization, although not always of ore grade. Within and around the zone of breccia pipes and mineralization there are a few faults and veins, but these are discontinuous random structures of minor significance. There are no regional or local systems of faults or other planar structures recognized which could account either for the mechanical development of the breccia pipes or for their localization as a group or as individuals. Hydrothermal alteration is pervasive in the zone of mineralization. Clay minerals appear to be abundant in places, but their percentages are undetermined. Quartz and sericite are the principal alteration products, and in many instances original rock textures are obliterated. The principal sulfides, hypogene pyrite and chalcopyrite and supergene chalcocite, occur mainly as vug fillings in the breccia and as small discrete grains scattered through all the altered rocks. Sulfide veinlets are relatively scarce. Sulfides are more abundant and alteration is more intense in certain rock units, such as the diorite and most of the breccias. Although the Toquepala mineral deposit is similar in most respects to the porphyry copper deposits of southwestern U. S., it most closely resembles the Braden deposit of Chile, as described by Lindgren

Jan 1, 1959

By C. R. Sandberg, L. S. Gournay, R. F. Sippel

The effect of fluid-flow rate and fluid viscosity on oil-water relative permeability determinations was studied using the "dynamic flow technique." In this work relative per-nleability curves were obtained for homogeneous small core .samples from several sandstorle outcrop form-utions. Radio-tracers were used for the determination of fluid saturation and for the detection of saturation gradients. Cobalt-60 in the form of cobaltous chloride was used as a water-phase tracer in some of the experiments. Iodine-131 in the form of iodobenzene and Mercury-20-3 in the form of mercury diphenyl were used as oil-phase tracers in other experiments. Flow rates for each phase were varied within a range of 2.5 to 140.6 ml/hr. Oil-phase vis-cosities under flowing condition,> were varied from 0.398 to 1.683 cp. The relative permbilities ob-tained were found to he solely a function of saturation and independent of flow rare, provided there was no .Saturation gradient induced in the core sample by "boundary effect." Even though equilibrium with re-sped to flowing conditions was obtained at the lower flow rates, where a saturation gradient exists, this equilibrium is of a "contingent"-type rather than the "steady-state" equi-librium implicit in the relative per-meability concept. The only effect of increasing the oil or non-wetting phase viscosity was to decrease the flow rate required for the elimina-tion of the boundary effect. Fairly good agreement between experimentally determined and calculated values of the boundary effect was obtained when the non-wet-ring oil phase was the only Flowing phase. INTRODUCTION In the characterization of reservoir rock, as well as in the solution of reservoir production problems, it is most desirable to have reliablc rela-tive permeability measurements for the rock and fluids of interest. Many techniques have been developed for the laboratory determination of the relative permeability of both large and small core samples. In varying degree, difficulties attend the use of all of the methods. Each of the methods requires the metered flow of fluids of known viscosity through the core sample under conditions wherein the pressure drop in the individual flowing phases can be measured or closely approximated. Since the relative permeability is a function of the saturation and distribution of the flowing fluids, some means of obtaining such information is also required. The laboratory determination of the relative permeability of a sample should give the same relative permeability saturation relationship that would exist if the sample were in place in the oil reservoir. The attainment of this objective is complicated by the fact that the use of small core samples for laboratory measurements is usually necessary. As a result, errors in measuring the relative permeability arise from boundary effects at either the fluid input or output ends of the sample; no significant boundary effect is anticipated at the sides of the sample normal to direction of fluid flow. At the input end of the sample a boundary effect exists if the flow fluids are not com- mingled as they would be in the reservoir. At the output end of the sample a boundary effect exists as a result of discontinuity of the capillary properties of the system. Here the flowing fluids leave the small flow channels and enter a collecting system having much enlarged flow channels. Thus, there is a tendency for the wetting phase to be retained by the core sample because of the attraction of the core sample for the wetting fluid. No reference is made to these boundary effects in either Darcy's equation or in the relative permeability concept. As a consequence the saturation effect peculiar to the input end of the core sample may cause an error in the effective permeability measurement, since some portion of the core sample must be utilized for commingling of the flow fluids. At the output portion of the core sample a saturation gradient or a saturation change along the axis of flow results. Since relative permeability is a function of fluid saturation, this saturation gradient may cause a variable permeability measurement, especially since extent and character of the saturation gradient can vary with fluid-flow rate. The most convenient method of minimizing the boundary effect, especially at the output end of the sample, is to flow the fluids of interest through the core sample at such high rates that the capillary forces arc insignificant as compared to the viscous forces involved in the fluid flow. Since recent work of a preliminary nature has indicated that fluid dispersion in the porous medium increases with the flow rate, the high flow minimizes the boundary effect at the input end of the core sample by enhancing the mixing of the fluids.

By V. B. Kurfman

Grain refinement of Mg-Al melts by carbonaceous additions has been attributed to nucleation by aluminum carbide. The effects of process and alloy variables are interpreted and predicted in terms of the dispersion and chemistry of this phase. The grain coarsening action of Be, Zr, Ti, R.E., chlorination, temperature extremes, and prolonged holding times is described. Measures necessary to insure an adequate dispersion of the catalyst are discussed. CARBON inoculation treatments have become fairly well known and used for grain refinement of magnesium alloys containing Al. Although there is general agreement that a nucleation process occurs, the process is not understood and the inoculants are used in a rather empirical fashion. The treatment is applied to the class of alloys containing 3 to 10 pct Al, i.e., AZ31A to AM100A. Typical methods involve melting, alloying, and adjusting the temperature to 1400° to 1450°F. Then 0.01 to 0.5 pct C as CaC2, C6C16, or lampblack is added by any convenient means, and the melt poured within 10 to 30 min. Investigators generally have been impressed by an assumed similarity of this refinement process to superheat grain refinement, which depends on heating approximately the same alloys to a temperature in the range of 1550" to 1650°F, then pouring promptly after the melt is cooled to the pouring temperature. Various predictions have been made that carbon refinement would replace superheating in commercial practice due to reduced process costs, but this replacement has not fully taken place because of production difficulties and conflicting observations. Davis, Eastwood, and DeHaven1 agree with Nelson2 and wood3 in suggesting that an excess of inoculant may be harmful. Wood however says that overtreat-ment is not a problem in production use of hexa-chlorobenzene inoculation, and Hultgren and Mitchell4 claim no evidence of harm from excess additions. Various grain coarsening reactions are known to occur, including the possibility of overtreatment mentioned above. Trace amounts of Be,2 Zr, and Ti may prevent refinement by either a carbon treatment or a superheat. Occasionally treatment with cl25 may cause coarsening, although the Battelle refinement process' uses a CC14-C12 blend. Grain coarsening also tends to occur on holding at temperatures below 1350°to 1400°F, especially after a superheat treatment, and for this reason Nelson2 stresses the desirability of a refinement method useful at lower temperatures for open pot melting practice. Since a carbon treatment can be made to work at temperatures below 1400°F, it seems desirable to investigate the mechanism of the refinement and the mechanisms of the coarsening reactions in order to establish control conditions for use in commercial production. The identity of the nucleating phase must first be established and then the factors affecting its chemistry and physical dispersion must be determined. THE IDENTITY OF THE NUCLEATING PHASE Davis, Eastwood, and DeHaven suggested that the nucleating phase in this system is Al4c3,1 but Mahoney, Tarr, and LeGrand8 disagree, largely because they found no evidence of the compound in alloys after carbon treatment and because there is no indication that aluminum carbide should be unstable over the temperature range used in the superheat treatment. This latter objection is based on the assumption that both the carbon treatment and the superheat treatment introduce the same nuclei. Electron diffraction studies have been made to identify the nucleating phase. Samples of grain refined A292 have been selectively etched SO that clean surfaces are obtained and so that secondary phases are in relief. Electron diffraction patterns from these surfaces have established that the carbon treatment of A292 introduces into the metal a large number of small, plate-like particles with a structure very similar to Al4C3. In most cases, the plate-like nature of the particles prevented positive identification but in the cases where the identification could be made the particles proved to be AIN A14C3. However, enough variation in lattice constants was observed so that all compositions from pure A14C3 to the 50:50 solid solution A1N.Al4C3 were probably present.14 In A14C3 and especially AlN.Al4C3 the A1 atoms occur in layers within which they have the same hexagonal symmetry and spacing as the Mg atoms in a single basal plane of a magnesium crystal. The solid solution spacing lies between the 3.16 of AIN and the 3.3? for Al4C3, in satisfactory agree-

Jan 1, 1962

By Paul Rhedey

Various commercial pelroleum cokes were heat-1,reated at temperatures between 500° and 1500°C, in a nitrogen atmosphere, in laboratovy induction furnaces. The rate of tenlperature rise was varied betzveen 10" and 300°C per min, or the green cokes were flash-calcined, orv a combination of heating rates was used. Changes in the rate of heating had only negligible effects on the degree of' calcination as characterized by mean crystallite thickness and the chemical properties of the calcined coke. The physical structure of the cake was however significantly affected when rate of heating during calcination exceeded 50°C per min over the temperature range of 600° to 900°C. Surface-accessible porosily increased with the .rate of temperature rise, and this was accompanied by a change in pore size distribution. Source and properties of the green coke also had an influence on the structure of the calcined coke. The evidence presented suggests a similar mechanism of porosity development in petroleuiiz coke during calcination in industvial equiplnenl, such as rotary kilns. An increase in surface accessible povosity incveased the pitch binder requirement when the coke was used as aggregate in Soderberg paste. A correlation was established between calcined coke porosity and paste binder requiremenl. ManY results have been published on the changes of properties of petroleum coke during calcination, such as chemical composition, real density, electrical resistivity, crystallite and pore structure. The correlation of these properties with temperature of calcination and time at maximum temperature has been rather well established in both laboratory and pilot plant experiments. Surprisingly little attention has been given however to the effect of calcination conditions, such as rate of temperature rise or furnace atmosphere, on the chemical and structural properties of the calcined coke. It has been observed that petroleum coke, when calcined in industrial equipment, acquires higher porosity and lower real density than those attainable in laboratory furnaces at apparently identical calcina- tion temperature and soaking time. This paper describes a study of the effect of rate of heating during calcination on calcined coke properties using green petroleum cokes of different volatile matter, hydrogen, and sulfur content. An attempt was made to correlate the changes in coke structure with the flowability of anode paste of the type normally used in aluminum reduction cells. EXPERIMENTAL Petroleum Cokes Used. In the study of release of volatile matter and sulfur during calcination and the effect of rate of heating on calcined coke properties two delayed cokes of different sulfur contents were used. The results of analysis of the green cokes are given in Table I. In the study of the effect of flash calcination thirty-six commercial petroleum cokes from twelve different refineries were used with a range of properties shown in Table 11. Calcination Conditions. Calcination experiments were carried out in a laboratory induction furnace. In each run a 200-g sample of dry green coke sized to 10 by 65 Tyler mesh was calcined in a graphite crucible. The crucible containing the sample was placed in the middle of a stack of eight others filled with metallurgical coke to reduce temperature gradients within the sample. Temperature was measured by two Pt, Pt-10 pct Rh thermocouples and controlled by a Celectray instrument. The two couples generally agreed within 5°C. In the study of volatile matter and sulfur release the samples were heated to temperatures in the range of 500" to 1500°C at a rate of 10°C per min in a nitrogen atmosphere and held at the final temperatures for 30 min. In the study of the effect of heating rate on calcined coke properties the desired rates between 10' and 300°C per min were obtained by manually adjusting the power input. Flash calcination was carried out by dropping 100 g of the green coke into the graphite dish preheated to the calcination temperature. Because of the small heat capacity of the furnace the coke was introduced in 20-g portions at a time. For this purpose a 2-in.-long nipple between two 1-in. gate valves installed on the top flange of the furnace served to provide a gas seal while feeding coke to the furnace. It was estimated that the temperature of the coke reached that of the furnace at a rate of approximately 1000°C per min. Holding time at final temperature was also 30 min. Calcined Coke Proper- Determined. Porosity was determined on 20 by 35 Tyler mesh samples using an Aminco-Winslow mercury pressure porosimeter with an operating range of 1.8 to 3000 psi absolute pressure (100 to 0.05 p pore diameter range).' Apparent density was obtained by the mercury poro-simeter. It represents a particle density of the 20 by

Jan 1, 1968

By C. B. Manula, R. Venkataramani

Application of computers to present-day open-pit mining with bucket wheel excavators (BWE) is discussed. The development of the wheel excavators and their use in mining are discussed along with the necessity for building a computer model of the bucket wheel and the mathematical formulation of the problem. The simulation procedure, testing the model, and test results are summarized. Even though the mining industry in 1966 produced more ore than ever before, current extraction rates are only a fraction of what is expected in the later years of the 20th century. Nearly 90% of all metals and mineral products consumed last year was recovered by open-pit mining. This has placed great pressure on this segment of the industry which has, consequently, resulted in some spectacular developments. With increasing size of projects, the need for increased sophistication of engineering, planning, management, and administration of modern mining installations has never become more apparent. The design of complete systems for the mine and plant that fit the mold of today's business and social environments is undergoing an evolutionary process. Traditional concepts in mine development and operations are being sidestepped in favor of new ideas and principles. As the overburden thickness increases, materials handling presents a major problem to mining companies, especially those concerned with the mass production of ore and waste from low-grade deposits. The profit margin here is likely to be significantly less as to take chances with capital investment. Constant efforts are needed to improve upon productivity if the ore is to be economically mined. The development of vast low-grade deposits and thick overburden deposits calls for better tools to handle the enormous amount of materials. A natural solution to this problem is the use of bucket wheel excavators (BWE), which employ a continuous cutting head to feed the materials handling system. High productivity, versatility, economy of operation, and adaptability to most types of haulage systems combine to make BWE's attractive for large earth-moving operations. "Operating costs are being pushed down by the impact of giant haulage units, by high-speed conveyors, and computerized railroads. Matching all these with the continuous output of BWEs, one can visualize increased production at much lower costs." Historical Background The wheel excavator, which was patented in Germany in 1913, made its first appearance in an open-pit lignite mine in 1920. From this early beginning, however, BWEs were slow coming into practice. Initial developments were dampened by many design problems. From 1936 onward, major developments in design improved the wheel's ability, capacity, and versatility. A literature survey shows that wheel excavators are being used in Australia, Zambia, South Africa, the Congo, India, Indonesia, Czechoslovakia, Russia, Great Britain, Guyana, Yugoslavia, Morocco, Germany, Canada, and the U.S. for mining and loading chalk, lignite, clay, sandstone, phosphate, broken ore of iron, coal, shale, loose and semi-loose rock overburden.' A recent LMG* BWE at work in a German lignite mine weighs 6790 tons with an hourly capacity of 11,000 cu m. Although the BWE has wide applicability, its application to new mining areas poses a problem. Because of the large capital investment involved in BWE application and the narrow profit margins in mining low-grade ores or coal at depth, little margin of error can be tolerated in the selection, design, and operation of these machines. The questions that need to be answered prior to installation of a BWE for a mineable deposit are: 1.) What are the anticipated BWE performance characteristics? 2) Which method of BWE operation is most efficient? Attempts to answer these questions require a thorough knowledge of the mining system and the BWE operation. One approach is the building of a computer-ori-ented simulation model to determine how information and policy create the character of the BWE system under consideration. BWE Operation Modern BWEs generally excavate in blocks. Fig. la shows a BWE working in an established cut. The wheel is positioned to travel on the pit floor in line with the top edge of the old highwall. As it advances, a new highwall is exposed in the direction of excavation. Digging is done by rotating the wheel, swinging it from side to side in long parallel arcs, and "crowding" into the bank, by advancing the entire machine, or by the travel of the digging boom if an automatic crowd is available (Fig. lb). A second way by which the wheel can be advanced into the bank is by the falling cut method. A brief description of each of these methods follows. Cut with a Crowding Machine: At the end of every swing, the digging boom can be extended by the thickness of cut desired and the boom swung back in the reverse direction. Obviously, the thickness of bank excavated does not vary with the boom position; therefore, the slewing motion of the boom is fairly constant for uniform output. The thickness through which the digging boom can be advanced into the bank is theoretically calculated from the formula'

Jan 1, 1971

ASHBEL WELCH, LAMBERTVILLE, N. J.: Dr. Dudley has given the wear of steel rails under four different conditions. He arrives at the conclusion that the softer rails, or those that from their composition ought to be softer, wear better than the harder. But there is another condition which has an important bearing on the subject, and, should not be overlooked,-the weight on a wheel. With the lighter weights of the past, the softer rails may have worn best; with the heavier weights of the future, the harder may wear best. Weights will probably be increased up to the capacity of steel to bear; then doubtless the harder steel will wear best. A leaden rail with ten pounds on a wheel might carry millions of tons, but with one hundred pounds on a wheel, it would be destroyed by a few thousand tons. So in the days of iron rails, my experience was that the softer rails under light machinery stood better than some of the harder; but under heavy machinery the softer were much the most rapidly destroyed. His doubtless the same with steel. The pounding motion of the wheels loosens or spreads the particles of a thin film of steel; the pull lengthwise on the rail de- * Metallurgical Review, vol. i, page 1. † The remarks as here given, as in the previous discussion on steel rails, have all been written out or revised by the participants in the discussion, and represent, therefore, their mature views. It has been thought that this plan, when it can be carried out without doing any of the speakers injustice in debate, is much to be preferred to a strictly verbatim report. The remarks of Mr. Chanute were sent to the secretary after the. meeting, and although they did not form a part of the actual discussion, there can be no doubt of the desirability of including them in this report. The papers under discussion were “Rail Specifications and Rail Inspection in Europe,” by C. P. Sandberg ; " The Wearing Capacity of Steel Rails in Relation to the Chemical Composition and Physical Properties," by C. B. Dudley, and a Rail Patterns," by A. L. Holley. T. M. D., Secretary.

Jan 1, 1881

By M. Baeyertr

Since 1915 many papers and books have covered industrial applications of X-rays from various angles. Two of the more recent are a paper by Fink and Archer, which describes in detail the technique of radiography, and a paper by Clark2, which embraces the whole field of X-ray metallogmphy. This paper, therefore, is confined to work of the X-ray Laboratory of the Western Electric Co., which naturally divides into two categories: radiography and diffraction patterns of various types. Radiography Radiography is the field in which the application of X-rays has had most general appeal among the industries which produce or use metals and alloys. Equipment permitting the examination of heavy sections of metals less permeable than aluminum or other light alloys requires apparatus capable of generating hard X-rays over a considerable period of time. The equipment used in the work presented in this paper is practically identical with that described by Fink and Archer in their paper on radiography in industry and is easily capable of penetrating 1/8 in. of lead. Radiography is used in two major groups of problems: (1) in the development of cquipment and tools and (2) in studies of materials. So far there has been no instance in which the use of radiography for routine inspection is justified. This is partly due to the fact that the manufacture of telephone apparatus involves the production of many identical parts by standardized procedures and equipment that has had development and trial before being put on a regular production basis. It is during this stage of development of equipment and tools that radiography has been used to particular advantage.

Jan 1, 1931

By C. D. Stahl, S. M. Farouq Ali

This investigation attempts to describe and simulate the alcohol displacement process by means of a cell model, as employed in chemical engineering practice. The proposed model is more simple than previously proposed models. and utilizes parameters chosen on a theoretical basis. The model successfully reproduced the formation of the stabilized bank and the breakthrough of alcohol, the latter depending on one of the model parameters, which may be correlated with the length of the porous medium. Moreover, the effects of the phase behavior of the liquid system involved, as observed in experimental studies, were reproduced. Several variations of the basic model were devised and tested on a digital computer. These included the cases in which: (1) the actual value of fractional flow was used in cell-to-cell computations; (2) the number of cells was varied within the same run; and (3) incomplete rather than complete phase equilibrium was assumed within each cell. The proposed cell model clarifies the basic mechanism of the process. Detailed concentration profiles obtained for each cell, for instance, showed the mechanism of bank formation in relation to the phase behavior characteristics. The results obtained indicated a varying degree of phase equilibrium concommitant with changes in the velocities of the phases in an actual alcohol displacement. This condition was approximated by changing the number of cells during the simulation. Interesting information was obtained on the influence of path length on the efficiency of alcohol displacement, which has been the subject of some controversy. Certain limitations preclude the use of the proposed model as a substitute for experimental studies. The results obtained were, nevertheless, of value in interpreting the experimental results. INTRODUCTION During recent years considerable effort has been directed toward an understanding of alcohol displacement, the process whereby oil and water are recovered from a porous medium by the continuous injection of a solvent. The complex nature of the physical process involved has so far defied a complete mathematical treatment. Other methods of approach, amounting to an overall material balance, have been proposed, yielding useful information on certain aspects of the process.1-3 Taber et al, in particular, defined the displacement mechanism in terms of the phase behavior of the alcohol-oil-brine system invoIved.2 Wachmann reported a mathematical treatment of alcohol displacement subject to certain simplifying assumptions? Donohue proposed the use of a "cell model" for simulating alcohol disPlacement.5 The nature of the assumptions involved limited the utility of the model. The present work attempts to examine the variables involved in the simulation of alcohol displacement and discusses several possible versions of the basic cell model. Under certain conditions the model results are similar to the experimental results. In particular, the spontaneous formation of of the stabilized bank and the effects of the system phase behavior were successfully reproduced. PREVIOUS WORK ON CELL MODELS Cell models and the theoretical plate concept are often used in solving chemical engineering problems in which an explicit mathematical solution may be difficult or impossible to obtain. Examples of such applications occur in distillation, gas-liquid chroma tography,6 reactor technology, absorption, etc. In petroleum engineering, such a model was used by Attra7 to describe non-equilibrium gas drive, and by Higgins and Leigh ton8 to calculate sweep efficiency in water flooding. Aris and Amundsen pointed out the equivalence between the diffusion model and perfectly mixed cells connected in series.9 Deans proposed a three-parameter cell model to simulate two-component

Jan 1, 1966

By Geoffrey Gilbert

A study of specimens shows that the key to both oxidation and enrichment at Duck-town is the behavior of pyrrhotite, which is in part dissolved and in part replaced by marcasite. Enrichment takes place chiefly at the expense of marcasite. THE material that forms the basis of this paper was collected in the spring of 1922, during a ten-day visit to Ducktown by the writer in the company of Prof. L. C. Graton. The time available for the work was far too short to allow anything like a thorough study of the deposits, and structural and stratigraphic questions, though they have an important bearing on the origin of the primary ores, were necessarily left untouched. Attention was focussed on the zone of oxidation and enrichment; and by devoting most of our time to the upper levels, open pits, and old workings, and examining the deeper levels only thoroughly enough to obtain a fair idea of the nature of the primary sulfide ore, we were able to make a reasonably complete survey of the various orebodies. With this field work for a background, the writer later made a study, in the Harvard laboratories, of the specimens obtained during the visit. As some of the facts brought to light by this study appear to be new, it seems worth while to set forth the outstanding features and a proposed explanation of them. Much of the Ducktown material that is obviously of greatest significance, as regards oxidation and enrichment, is soft and crumbly. Notwithstanding the desirability of gaining from such material all possible information as to its mineral composition and textural relationships, but little has heretofore been learned regarding it; but, by suitable preparation of this material in connection with the present study, it has been possible to examine it under the microscope without any disturbance of its texture and about as satisfactorily as if it were hard, fresh ore. The information thus gained has contributed measurably to the results set forth in this paper.

Jan 3, 1924

By Philip Bucky

THE general conception of a mine model is that of a three-dimensional object representing the mine workings, the orebody and the country rock of a particular property. Its chief uses have been to make it easier to understand the mine and to serve as a basis for the arguing of legal questions. Fayol endeavored to use mine models in a different way and to all students of subsidence "Fayol's dome theory" is of decided interest. We have more recently the suggestion of Young and Stoek of the University of Illinois, who1 suggest the use of models as a means of studying the problem. Prof. Henry Briggs, of the University of Edinburgh and Herriott Watt College, also makes use of models to determine the effects of bending at the edges of extensive workings.2 It is interesting to note that civil engineers are taking a decided interest in the application of models and the principles of dynamic similarity to the solution of their problems. The Proceedings of the American Society of Civil Engineers for 1930 contain an elaborate article by Benjamin F. Groat,3 who says, in his opening remarks: "Every engineer should know and understand that a model constructed in accordance with Newton's theory of similarity is not only the means for reproducing the complexities of flow, or other mechanical action, on a small scale, but that models may be made the best means of designing works of great magnitude. In the present state of knowledge, a properly constructed and properly tested model will answer the difficult questions of hydrodynamics much more quickly and accurately than the most profound mathematical analyses." A study of P. W. Bridgman's book on Dimensional Analyses leads one to arrive at the same conclusion.

Jan 1, 1931

By C. Gatlin, M. E. Chenevert

The effects of bedding plane orientation on the elastic constants and the yield strengths of three laminated rocks (one sandstone and two shales) and one isotropic rock (a limestone) were studied. The directional dependence of the elastic properties of these rocks was experimentally evaluated using a triaxial compression cell and auxiliary stress-strain measuring equipment. Symmetry of Poisson's ratios within the bedding plane suggested that horizontal isotropy exists, but the bedding planes do give rise to an appreciable difference between properties in the horizontal and vertical directions. For the three bedded rocks studied, Young's modulus was lower normal to bedding than along bedding. Yield strengths were determined at confining pressures from 0 to 12,000 psi in a triaxial compression cell. The rocks studied showed strength reductions as high as 40 per cent when the test specimen was oriented at 20°-30° to the bedding planes. The mechanical behavior of these rocks suggested that the rock properties of shear strength and/or coefficient of internal friction can vary with direction, depending on the particular rock tested. Tensile strengths were also measured and found to be lowest when failure occurred along bedding. This work shows that bedded formations exhibit sizable directional variations in both their elastic constants and yield strengths. It is suggested that these variations may be accounted for by using the "elastic laminate" model and the "variable coefficients" failure model. INTRODUCTION The nature of rock deformation at elevated pressures has been studied by many workers; papers by Handin,l,2 and Robinson3 illustrate the present state of knowledge. Most investigators have either chosen rocks which were as isotropic as possible (in order to avoid complications of data interpretation and analysis) or they have oriented their samples so that the effects of anisotropies (such as bedding planes) have been avoided. Of the studies performed, few were concerned specifically with mechanical anisotrop-ies. Griggs4 has presented limited data for specimens cut parallel, normal, and 45° to the bedding plane; he relates the strength anisotropy observed to the fabric (bedding) anisotropy. His tests were primarily concerned with large deformations (20 per cent strain); thus, no directional values of the elastic constants were reported. Handin has reported the results of similar experiments. Bott5has discussed rock strength anisotropies due to faults, cleavage, or bedding. He was concerned primari ly with determining the shear stress on such planes and did not mention the effect of friction. Jaeger6 later generalized Bott's work by taking friction into account and presented a limited theory for the failure of rocks having a "single plane of weakness", and also for rocks having a constant coefficient of friction, and a shear strength which varies with bedding plane orientation. Donath and Cohen,7 and Donathg have evaluated rock strengths from shale and slate specimens cut normal and parallel to bedding. A dependence of cohesive strength (7,) on the specimen orientation was also shown. Adler9 has also studied this problem and lists similar results. He assumes that all bedded rocks behave according to Jaeger's single-plane-of-weakness theory. Kalinin and Belorussov10 list results for strength tests parallel and perpendicular to bedding and use this information as a basis for hole deviation analysis. From the literature it is apparent that sedimentary rocks have been tested under widely varying conditions of stress; however, the assumption of isotropy is generally, but not always, made. Since geologic sedimentation often deposits sediments in very definite lavers.,. it seems that more svstema tic attention should be given to the possible effects of this natural bedding. Bedding, as used here, refers to visible regularities of grain size or orientation resulting from depositional processes. The mechanical strength anisotropies, which bedding may present, is not the only anisotronic property to be considered, since the elastic

Jan 1, 1966

By J. R. Long, C. E. Armantrout, A. H. Roberson, T. R. Graham, R. S. Dean

THE general program of the Federal Bureau of Mines on the study of alloys made with electrolytic manganese has been extended to copper-manganese-aluminum alloys. The initial results of the work are presented in this report and concern a determination of the mutual solubilities of these three metals to form the alpha solid solution. The principal studies of this system, reported in the literature, have been focused on the Heusler alloys containing 10 to 30 per cent Mn with 9 to 15 per cent Al. These investigations concern the ferromagnetic properties and the determination of the crystallization contours, with little emphasis on the phases present in the solid state outside of this area. Heusler1 recognized a breakdown of the beta solid solution of the magnetic alloy, which he says decomposes into the alpha, beta, and gamma phases of the copper-aluminum system, somewhat modified by the presence of manganese. Rosenhain and Lantsberry2 examined alloys ranging up to 10 per cent Mn and io per cent Al but were unable to reach definite conclusions concerning the phase boundaries in that area. Krings and Ostmann3 made magnetic studies and examined the system by thermal analysis. They present contours of the liquidus surface but do not place any of the phase boundaries. Corson4 [ ] has drawn a hypothetical boundary for the alpha field with few data to support such construction. The binary systems involved have received considerable attention by numerous investigators, and their general features are well established. The hopper-aluminum system (Fig, I) has been thoroughly examined by Stockdale,5 who places the limit of solubility of aluminum in copper at 7.4 per cent at the liquidus and 9.5 per cent at room temperature. Smiths established the eutectoid temperature at 570°C. by a study of isothermal decomposition of the beta phase. The copper-manganese system (Fig. 2) has been recently reviewed by Dean and co-workers.7 Using high-purity alloys, they place the solubility of alpha man-

Jan 1, 1946

By A. S. Odeh

The mechanism of two-phase flow in porous media has been a subject of wide controversy. One of the properties essential for understanding the dynamic behavior of two-phase flow is relalive permeability. Relative permeability to a certain phase is defined as the ratio of the effective permeability of that phase to its permeability when it is the only fluid present and powing. In this research, a theoretical analysis was made to determine the effect of viscosity ratio between the non-wetting and the wetting phase on relative permeability. Experimental work was conducted to test the validity of the derived equations. The experiment was conducted on four natural cores. Four oils were used as the non-wetting phases with a viscosity range of 0.42 to 71.30 cp and two wetting phases with a viscosity range of 0.86 to 0.96 cp. Oil and bring were made to flow simultaneously at various ratios, and relative permeability curves were constructed. A total of eight relative pertileability cycles representing eight viscosity ratios were run oil each sample. It was found that relative permeability to the non-~cletting phase varies with viscosity ratio. The relative effect of this variation on relative permeability values was a function of the sample's single-phase permeability, decreasing with its increase. It was concluded that, for .samples of single-phase permeability over I darcy. the effect of viscosity ratio could be disregarded, and relative permeability would be, in effect, a function of satrtration only. INTRODUCTION Two-phase as well as multiphase flow occurs in many fields of science. This type of flow is of particular interest in petroleum production. The knowledge of relative permeability, which describes the dynamic behavior of two-phasc as well as multiphase flow, is essential for solution of problems arising in that field. Thc relative permeability ot a porous medium to a given phase in multiphase flow. is generally considered to be only a function of the saturation of that phase, independent of the properties of fluids involved and ranging in value from zero to unity. Work by Leverett' and Leverett and Lewis' apparently supports this concept. In his experiments Leverett used a clean, packed unconsolidated sand of high permeability (3.2 to 6.2 darcies) with two phases (water and oil) flowing and a viscosity ratio range of 0.057 to 90.0. His results showed that the wide range of viscosity had practically no effect on relative permeability-saturation relationship. Recently accumulated evidence from work performed by several laboratories and a paper by Nowak and Krueger,2 in which relative permeability to oil of a few core samples in the presence of interstitial water was considerably greater than single-phase permeability to water, cast some doubt on the conclusions reached by Leverett' and subscribed to by a large number of individuals in the oil industry. One explanation advanced to explain this behavior states that it is caused by the variable extent of hydra-tion of clay minerals present in the sand. The greater the water saturation, the greater will be the area of contact between water and clay minerals; therefore, the greater will be the extent of swelling with corresponding reduction in permeability. Yuster4 presents another explanation for the recently accumulated evidence. Utilizing Poiseuille's law, he analyzed concentric flow in a single capillary where the non-wetting phase flows in a cylindrical portion of the capillary and concentric with it. The wetting phase flows in the annulus between the non-wetting phase and the capillary wall. The equations obtained indicate that relative permeability to the non-wetting phase is a function of saturation and viscosity ratio. Although Yuster's equations show that fractional rel-ative permeability to oil could be greater than unity, as was indicated by the data of Nowak and Krueger,1 they failed to present an explanation to the experimental data of early investigators such as Leverett.1 Due to the importance of relative permeability in understanding the flow behavior of petroleum reservoir fluids, this work—theoretical as well as experimental —was undertaken to determine whether relative permeability is a function of saturation only as was concluded by Leverett1 or a function of saturation and viscosity ratio as was theorized by Yuster.4 THEORETICAL ANALYSIS An equation will be derived for the rate of oil flow through a porous medium that is initially filled with water. Based on this equation, an analytic expression for relative permeability will be developed. The porous medium will be assumed to consist of .straight circular capillaries of different radii. It will also be assumed that there are no interconnections among the capillaries and no mass transfer across the oil-water interface. Consider a porous sample initially saturated with a wetting phase (water). As a non-wetting phase (oil) is

By Hans-Jürgen Schaller, Horst A. Brodowsky

Activity coefficients of boron in palladium were determined at concentrations up to PdB0.23 by reducing B2O3 between 870" and 1050°C in a controlled H2-H2stream and measuring the resulting weight gain. The deviations from ideal behavior closely resemble those of the system Pd-H and are interpreted in terms of three principles: 1) The solute atoms occupy octahedral interstitial positions. 2) They donate their valence electrons to the 4 d and 5s bands of palladium, raising its Fermi energy. 3) The lattice strain energy is lower for two nearesl -neighbor interstitial particles than for two farther separate ones. SOLID solutions of hydrogen in palladium are a useful subject for studying thermodynamic aspects of the formation of alloys and of nonstoichiometric systems.1-3 The activity of hydrogen is readily measurable to a high degree of accuracy,4'5 even at low temperatures where the deviations from ideal behavior are more pronounced, and its simple structure facilitates an interpretation of these deviations in terms of a detailed model. Two effects are discussed to account for the non-ideal properties:3 An "electronic" effect, connected with the rise of the Fermi energy, as electrons of the interstitial hydrogen atoms enter the electron gas of the metal, and an "elastic" effect, due to an interaction of the regions of strain around each interstitial atom. The electronic effect is based on the idea that the lowest energy levels of the dissolved hydrogen atoms are higher than the Fermi energy, so that the electron will not occupy a localized state but enter into the electron band of the metal.6 The elastic effect is based on the observation that dissolved hydrogen distorts and expands the palladium lattice. The hypothesis is put forward that the elastic strain energy is lower for two adjacent dilatational centers than for two separate ones; i.e., they attract each other. The resulting pair interaction can be used to calculate an elastic contribution to the thermodynamic excess functions by means of one of the statistical methods. This model permitted a detailed description of the solution properties of hydrogen in palladium3 and in palladium alloys.798 An extension of the approach to describe the excess functions of substitutional palladium alloys is possible.9 In order to further test and refine the model, an investigation of other interstitial alloys was started. Palladium dissolves considerable amounts of boron in homogeneous solid solution.10 The palladium lattice expands linearly up to nB = 0.23 (nB = B/Pd atomic ratio), the highest concentration studied." The expan- sion, extrapolated for 1 mole of interstitial per mole of palladium, is 17 pct of the lattice constant of pure palladium vs 5.7 pct in the case of hydrogen.12 The fact that the lattice expands rather than contracts is a strong indication that interstitial positions are occupied. According to neutron diffraction experiments, hydrogen occupies the octahedral sites of the fcc lattice.13 Unfortunately, this direct evidence is not available for the Pb-B system, mainly because of the high-reaction cross section of boron with thermal neutrons. However, by way of analogy and on the grounds of the rather close similarities between the two systems to be reported here, it seems safe to attribute octahedral positions to the dissolved boron, too. At higher boron contents, compounds of stoichiomet-ric compositions are reported such as Pd3B, which has the structure of cementite,14 so that a close structural relationship seems to exist with the system r Fe-C. In their study of hydrogen absorption in Pb-B alloys, Sieverts and Briining noted that alloys with an atomic ratio of about nB = 0.16 are no longer homogeneous15 This observation was confirmed in an extensive X-ray investigation.11,16 The phase boundaries of two miscibility gaps were established. One two-phase region was stable below a transition temperature of about 315°C and extended from nB = 0.015 to 0.178. The other one extended from nB = 0.021 to 0.114 slightly above the transition temperature and had an apex at nB = 0.065 and 410°C. All phases involved have the fcc structure of pure palladium with lattice expansions proportional to their boron contents. The occurrence of miscibility gaps, i.e., the coexistence of dilute and concentrated phases, points to an energy of attraction between the dissolved particles, in the Pb-B system as well as in the Pd-H system. The filling up of the electron bands seems to be analogous, too, in the two systems, as indicated by the hydrogen absorption capacit15,17,18 and by the suscepti bility of Pd-B alloys.l8 In both types of experiments, boron acts as an electron donor. A chemical method was used to measure the activity of boron in palladium. Boron trioxide was reduced in a moist hydrogen stream: B2O3 + 3H2 = 2B + 3H3O [l] At known activities or partial pressures of boron trioxide, hydrogen, and water, the activity of boron could be calculated from the law of mass action. The equilibrium concentration of boron corresponding to this activity was determined as the weight gain of the sample. EXPERIMENTAL The samples consisted of small pieces of foil of 0.1 mm thickness and about 100 mg weight. The palladium was supplied by DEGUSSA, Germany, and stated to be

Jan 1, 1970

By R. W. Raymond

THE absence of a convenient glossary of terms connected with mining and metallurgy has long been felt by the general public. It is to meet this want, not to furnish a technical manual for experts, that the following glossary has been prepared. It originated in an attempt on my part to revise for publication the manuscript of a compilation prepared from the appendix of Yale's work on Mining Titles and one or two other sources, to serve as an appendix to a new work on mining law, about to be published by Mr. H. N. Copp, of Washington, D. C. This revision soon assumed, contrary to my original intention, the proportions of a reconstruction; and with the consent of Mr. Copp, and for the purpose of receiving from my fellow-members valuable aid, I presented my still incomplete work as a paper at the Lake Superior meeting of the Institute, inviting from any quarter suggestions of new terms or better definitions to be incorporated in the glossary before its final publication. This invitation was so widely and generously responded to, that I cannot undertake to make in this place individual acknowledgments to those members of the Institute, and professional colleagues outside of it, who have favored me with assistance and advice. The labor bestowed upon this paper since its presentation at the Lake Superior meeting has considerably exceeded that of its first preparation, as may be inferred from its great increase in length, as well as the numerous alterations which it has undergone. It could certainly be still further enlarged and improved; but I think a comparison of it with any of the glossaries of the same class now in print will show, at least, that it is an advance upon what has hitherto been accomplished. 1 shall be grateful, however, for further criticisms and suggestions; and I purpose at some future time to incorporate in a supplementary paper the results of such additional collections or corrections as I may obtain. To avoid too great prolixity, I adopted at the outset the following general principles: 1. To include the most important technical words and phrases used by American miners and metallurgists, or occurring in English books and periodicals.

Jan 1, 1881

By A. Perry Thompson

I- GeneRal Distribution, AppeaRance, and Relations ........ 563 11. Data fRom MicRoscopic Examination............... 568 1. Criteria for Distinguishing Primary from Secondary Minerals...... 568 2. The Leonard Vein Filling..................... 574 Quartz............................ 575 Pyrite............................ 575 Enargite............................ 576 Covellite............................ 578 Bornite............................ 581 Chalcocite........................... 583 Chalcopyrite.......................... 586 3. The Fault-Vein Covellite..................... 587 The Speculator Ore........................ 587 The East Gray Rock Ore.....,.............. 589 4. Other Occurrences of Covellite.................. 591 111. Conclusions........................... 592 1. The Replacement of Minerals..................592 2. The Character of Mineralizing Solutions .............. 594 I. General Distribution, Appearance, and Relations Mining in Butte has seldom encountered covellite in commercial quantities. The notable occurrences, extending vertically and laterally perhaps several hundred feet, presented scattered, bladed lenses of this mineral in a matrix of quartz, pyrite, enargite, bornite, and chalcocite. But under the microscope covellite is seen to be widespread in the Butte ores, though in such small quantity that megascopic examination will not discover it. In early mining operations covellite was found in the Gray Rock vein, a member of the Blue vein system. As described by Sales,' it persisted as an occasional ore mineral, associated with quartz, pyrite, tetrahedrite, bornite, chalcocite, and minor amounts of sphalerite, from the 700-ft. to the 1,200-ft. level of the East Gray Rock and Diamond mines. Crushed quartz-monzonite and later quartz completed the vein filling between

Jan 1, 1916

By A. A. Blow

The productive area of the Leadville mining district immediately adjoining the city of Leadville, which, by its wonderful richness, has attracted the attention of the mining world for the past twelve years, may, with a few exceptions, he considered as divided into seven local mining centers, separated one from another by the topographical features of the country, and designated by common consent as Fryer Hill, Yankee Hill, Breece Hill, Rock Mill, Printer-Boy Hill, Iron Hill, and Carbonate Hill. Of these seven distinot mining localities, or groups of mines, the central one, Iron Hill, is the one of greatest importance and interest. It was the scene of the earliest discovery of carbonates, as far back as 1875, and since that time has always maintained its position

Jan 1, 1890

By H. H. Rachford

Numerical solutions of immiscible flow problems in which dispersive effects of capillarity are dominated by convection require excessively fine grid spacing with attendant high computing costs. The use of coarser spacing reduces cost but often produces oscillation or undue dispersion associated with displacement fronts, A numerical formulation is proposed here which should be applicable to two-dimensional flow problems. it is in part analogous to an approach previously tested for miscible systems. The convective transport is approximated using a change of variables to yield a coordinate system moving approximately with the local characteristic velocity. The capillarity-induced dispersive terms in the differential system describing the process are approximated with respect to a fixed coordinate system by the usual implicit formulation. One-dimensional tests of the procedure yielded results in which the saturation profiles tended smoothly to the zero-capillary pressure solution as the ratio of viscous to capillary forces was successively increased in a sequence of calculations. This contrasted favorably with solutions by other numerical procedures which would require attendant grid refinements to approach the zero capillary pressure results. INTRODUCTION Numerical solution of displacement problems has until recently relied on applying methods developed primarily for transient heat-flow problems. Such problems are classified as parabolic in type, and where the heat transport is purely by diffusion their solutions are characterized by a high degree of smoothness. It is not surprising, therefore, that for approximating these solutions available finite difference methods are quite adequate. In flow problems the transport is partly by diffusion, partly by convection or flow. Although the problem remains of parabolic type because the dispersive effects of capillary forces or diffusion play some role in every displacement, at high flow rates the problem is dominated by convection, and solutions tend toward those of equations of the hyperbolic type. Solutions of hyperbolic problems are characterized by the translation of fronts, or discontinuities, that may progressively increase in sharpness. Numerical methods for treating parabolic problems become less and less satisfactory as displacement rates increase and the role of dispersion due to concentration or capillary pressure gradients becomes small relative to transport due to flow. In computation the difficulty manifests itself as an error associated with the grid size chosen. 1-6 In summary, if the heat-flow type approximations are to include the terms arising due to convection, one of several choices may be made: (1) an upstream (to the direction of flow) approximation for the convection terms may be used; (2) a centered-in-distance (CID) approximation may be used; or (3) a recently developed approximation based on the theory of oscillation matrices may be chosen.6 The last appears to have significant promise for one-dimensional flow problems; its extendibility to two or three dimensions is an open question. In either of the first two approaches, a suitably small ratio of v&/D must be maintained, where v is the velocity, & is the grid spacing and D the effective dispersivity in the direction of flow. In the first choice, the approximation of the convective part is only first-order correct and errors introduced appear as a numerically induced dispersivity of magnitude proportional to v?x. In the CID choice, the approximation can be second-order correct, but the difference formulation fails to satisfy the maximum principle unless a condition on v?x/D is met. Practically, this means that for high flow rates oscillatory solutions may result in the neighborhood of a front unless exceedingly small grid intervals are taken. While the procedure proposed by Stone and Brian4 permits a less severe limitation to be placed on this ratio, ultimately the flow rates increase relative to the dispersivity the oscillation obtains. Further, extensions of their approach to higher dimensional systems may be attended by considerable

Jan 1, 1967