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By Jack Green

Within three major tectonic time frames of earth history: Microplate (±3.8 - ±2.6 billion years), intraplate (±2.6 - ±1.3 b.y.), and macroplate (=1.3 b.y. - present), precious - metal deposits are confined to specific structural, depositional and physico-chemical environments. Precambrian primary gold deposits are localized in two microplate greenstone episodes (±3.7 and ±2.7 b.y.); secondary gold in Witwatersrand placers (±2.6 b.y.). Precambrian primary platinum group metals are in anorthositic facies of layered mafic intrusions (±2.8, ±1.8 and ±1.0 b.y.). Most radioisotope mineral dates cluster - at these times and are coincident with inflections on polar wandering curves. These coincidences may reflect episodicity in lunar tidal disruptions and global deceleration effects in crust and outer core during micro- and intra- plate phases. Macroplate tectonics and an oxygenated atmosphere created favorable conditions for strata-hosted and plate suture gold and silver deposits. "Black smokers" at constructive plate margins and calc-alkalic calderas at destructive plate margins are loci for hydrothermal gold and silver.

Jan 1, 1984

By J. Moore, D. Gault, R. V. Lugn

Impact of small projectiles with velocities between 0.9 and 7.3 km per sec on basalt produce craters chiefly by the ejection of fragments. Weight-size distributions of the ejecta are linear for part of the size range of the fragments. Cumulative weight-size distributions of the ejecta from different craters vary because of erratic formation of large fragments and a large percentage of ejecta below 0.1 mm. In the range of velocities studied, the crater depth is approximately proportional to the 0.75 power of velocity of the projectile. This relationship may represent a transition regime between the fluid impact regime and the undeformed projectile impact regime. The volumes per unit of projectile energy of the craters produced are comparable to those reported for lower speed projectile impact and drill bits. An experimental investigation of projectile impact on rock is being conducted jointly by the Ames Research Center of the National Aeronautics and Space Administration and the U.S. Geological Survey. Projectiles are launched with light-gas guns at the Ballistics Range of the Ames Research Center. The craters and ejecta produced in these experiments are being studied by the U.S. Geological Survey. Steel, aluminum and polyethylene projectiles weighing from 0.25 to 0.015 g were accelerated to velocities of 0.88 km per sec (2,900 fps) to 7.3 km per sec (24,000 fps) with a light-gas gun, using hydrogen as the propellant medium. Projectiles impacted the targets normal to plane rock surfaces in an atmosphere of air with a nominal pressure of 25 to 50 mm of mercury. The metal projectiles were mounted in supporting four-piece nylon sabots, which guided the projectiles down the launching tube. After launch, aerodynamic drag acted to separate the sabots from the projectiles. Impact velocities were determined with time measurements and spark photographs of the projectiles in flight. Ejecta were collected in lucite and aluminum containers placed around the target block. A small hole in the containers permitted projectile entry. Impact of projectiles of the size employed produced craters in the rock targets chiefly by ejection of fragments. The craters are small, roughly conical depressions with crushed and intensely fractured rock at the bottoms of the depressions. The ejecta are composed of pieces of the projectile and rock fragments ranging in size from a few tenths of a micron or less to several centimeters in maximum dimension. In this paper, the structural features of the craters, the weight-size distributions of the recovered ejecta, and crater depth and crater volume relationships are described. DESCRIPTION OF CRATERS Typical craters (Fig. 1) produced by experimental projectile impact in basalt are shallow, wide base

Jan 1, 1963

By Bradley Stoughton

(Cleveland Meeting, October, 1912.) [SECRETARY'S NOTE.-To avoid repetition of foot-notes, references to authorities are made in this paper by means of figures, referring to a numbered list in the appendix.-J. S.] INTRODUCTION. THIS paper gives the results : first, of a research into the somewhat extensive literature of titanium; and second, of a series of original tests upon the effect of titanium on iron castings. New investigations have also been made upon the effect of titanium on steel, but I hope to treat this subject in an independent paper at some later date, and, therefore, will not discuss the experiments in detail here. The combined results of this study, which extended over a period of more than two years, can be briefly summarized as follows: 1. Steel or cast-iron, in which the titanium is properly proportioned, and which has been properly treated, is improved in strength, toughness, and durability against wear, such as, for example, the wear of railroad-rails, of steel and chilled-iron .rolls, car-wheels, etc. 2. These improvements seem to be caused, not so much by the direct effect of titanium on the metal, as by its cleansing influence in removing harmful impurities, such as oxygen and oxides, nitrogen, occluded slags, and perhaps also sulphur. It appears also to reduce segregation, which would contribute to the same end. 3. In order that its effects may be fully realized, the treatment of steel or iron with titanium must be correctly performed. There are a few simple, but essential, details to be observed; if they are neglected, the best results cannot be expected. To illustrate by an example : A series of tests on cast iron

Nov 1, 1912

By Morris M. Fine, Norwood B. Melcher

It is out of the question, at this time, to select any one prereduction process as superior to the others. It is apparent that several share a basic similarity and that within the groups listed in Part 1, the reduction vessel is sometimes the only significant variable. Claims as to the virtues of one machine over another are difficult to substantiate: one may be rapid, another thermally frugal. Based on published data, however, all seem to be performing adequately. It would appear that processes based on carbonized pellets are most applicable to foundry iron at low production rates. Adaptation to large scale manufacture of blast furnace hot metal or to agglomeration of fine concentrates at the mine site is much less likely.

Jan 8, 1966

By E. J. Dulis, A. Kasak, R. C. Westgren

The potential of uirought tungsten- and tantaluw-rich alloys of the W-Ta-Mo-Cb system was investigated for high-strength structural applications above 2500° F. Appreciable strengthening of tung-sten and tantalum—essentially attributable to solid-solzction effects—was obtained with binary, ternary, and quaternary alloys. Tensile strengths as high as 67,000 psi were achieved at 3000 OF. ThE quest for wrought structural materials which possess good strength properties at temperatures above 2000°F has led to a considerable research effort during the past decade. In addition to exploring the potential of various high-melting-point refractory metals (such as molybdenum, columbium, tantalum, and tungsten) for very high-temperature structural applications, alloy-development programs have been undertaken to achieve greater strengths than could be achieved with unalloyed refractory metals. The methods of strengthening refractory metal alloys have included both solid-solution and dispersion strengthening. General relationships among the relevant properties (melting point, recrystallization temperature, and high-temperature strength) of refractory metals indicate that the highest strengths at temperatures of 2500°F or higher would be obtained with tungsten-or tantalum-base alloys. Therefore, the present investigation was undertaken to determine the high-temperature strength potential of solid-solution strengthened alloys based on the binary system W-Ta; to effect further strengthening, minor additions of molybdenum and columbium (at the 6 and 12 pct levels) were made. The portion of the W-Ta-Mo-Cb quaternary alloy system of interest is shown schematically in Fig. 1. The component metals—W, Ta, Mo, and Cb—have a bcc structure at all temperatures, and their binary systems are mutually completely soluble.' Complete solid solubility in the W-Ta-Mo and W-Ta-Cb alloy systems has been demonstrated,' and, therefore, it was expected that the quarternary alloys of the system would also exhibit complete solid solubility at all temperatures. In the virtual absence of contamination by interstitial elements, all the alloys would be truly solid-solution strengthened. Twenty specific compositions of this investigation included binary, ternary, and quaternary alloys of the W-Ta-Mo-Cb system as well as unalloyed tungsten and tantalum. The compositions are shown in Table I. EXPERIMENTAL PROCEDURE Consumable-electrode vacuum-arc melting with ac power was used to produce small laboratory-sized, cylindrically shaped ingots (1-1/4 in. in diameter and 2 to 3-1/2 in. long) of the twenty compositions. A furnace was specially constructed to melt as many as four electrode rods simultaneously into molds lined with tungsten or tantalum sheet. High-purity rods of tungsten, tantalum, molybdenum, and columbium were used for consumable electrodes; the diameter of each rod was determined by the desired weight percentage of the component metal in a given alloy. The details of the construction and operation of the melting furnace will be discussed in another p~blication.

Jan 1, 1964

By F. F. Skiba, P. J. Root

A mathematical model has been used to investigate crossflow effects in a stratified reservoir during an idealized displacement process. A process in which one incompressible fluid displaces completely another incompressible fluid of the same density and viscosity was considered. The reservoir was assumed to be composed of homogeneous layers which are discrete but interconnected. Approximate five-spot flow geometry was simulated by arranging two pie-shaped cylindrical (two-dimensional) wedges in series. Some of the common production methods rely, for their effectiveness, on the fact that the formation consists of isolated strata. This is particularly true of selective plugging and single-zone production-injection methods. The effectiveness of these techniques for several cases in which adjacent strata are in communication has been evaluated. The usual production-injection schemes for fluid injection processes involve using the same completion interval in both the production and the injection wells. The efficiency of this, as well as alternative productioz-injection procedures has been examined for some cases involving communicating strata. INTRODUCTION The performance of many fluid injection projects is marred by early breakthrough and by production of a high percentage of the displacing phase after breakthrough. This channeling effect, if it occurs in reservoirs which have large permeability variations, is often explained on the basis of a model composed of discrete, isolated strata. Corrective or preventive measures based on this same model are also common. The behavior of stratified models has been the subject of considerable study. An excellent review of the early literature was given by Seba.1 Studies of the depletion performance have since been made for continuous, unrestricted communication between strata2-4 and for production from one permeable bed in continuous but restricted communication with an adjacent permeable bed.5,6 Model studies of displacement processes in stratified systems with crossflow also have been reprted.7-12 Finally, methods which account for crossflow have been developed for computing displacement behavior in stratified systems.13,14 Most methods for controlling or preventing channeling involve some change in the interval open to production and/or injection. Although many variations of the selective completion problem have been studied in regard to the depletion of a reservoir, little attention has been given to the behavior of a displacement process under similar conditions. Sebal used a resistance network model to study the performance of a process in which one incompressible fluid displaces an identical fluid from a linear, stratified reservoir. He investigated the possibility of improving the vertical coverage by limiting the completion interval of the production well. This investigation deals with techniques in which selective completion of the production and/or the injection wells is used in an attempt to control channeling. At one extreme, selective plugging and single-zone isolation (assuming perfect execution) should be successful if the reservoir is actually made up of independent strata. At the other extreme, they can hardly be expected to be successful if the channeling is caused by a mechanism in which stratification effects are negligible even though there are extreme variations in the formation permeability and/or the injectivity profile of the wells is not uniform. By contrast, it is difficult to anticipate the effect that the amount of communication between the beds of a stratified system will have on the efficiency of selective completion techniques. The objective of this study is the quantitative determination of the effect of communication on the behavior of some particular stratified systems which will at least lead to qualitative conclusions.

Jan 1, 1966

By A. S. Argon, G. East

From their study of the anisotropy of grain boundary mobility in aluminum, the authors conclude that tilt boundaries have a higher mobility than twist boundaries because the atomic misfit at the pure-twist boundary is relatively small compared to the misfit at a tilt boundary for a given amount of misorientation. If this is true, then one would expect a twist boundary to have a lower grain boundary energy than the corresponding tilt boundary. Fig. 6, taken from the work of Gjostein and Rhines,10 shows that this is indeed the case for [001]-cu tilt and twist boundaries in the high-angle region, thus lending support to the authors' conclusion.

Jan 1, 1968

By G. H. Wigton

THE oxidized ores of the Chief Consolidated Mining Co., in the Tintic mining district, have never yielded to metallurgical treatment by any standard method except smelting. These ores occur in comparatively small, irregular, siliceous replacements in limestone, and carry silver, lead, and gold as the principal valuable metals. But smelting methods. are unsatisfactory, as the lead smelters heavily penalize the large amount of silica in the ore, and the copper smelters do not pay for the lead in the ore; therefore, an alternative treatment method was sought. In 1916, a metallurgical research department was organized under; the direction of the writer. Many standard metallurgical methods were investigated but, on oxidized ore, none yielded extraction great enough to make its use feasible. During some chloridizing-roasting experiments in 1916, made in an assay muffle, the writer noted that large proportions of the silver, lead, and gold were volatilized from certain oxidized ores. The possibility of volatilizing the metals and collecting them in the form of a concentrated fume was then studied. But, as it was shown that satisfactory chloride-volatilization would be limited to a furnace feed with a high fusing temperature of the non-volatilizable constituents, and as the results obtained in a rotary kiln with the admixture of common salt with the ground ore were inferior to muffle tests, further volatilization experiments were discontinued until 1920. During this interval, an experimental sulfidizing and flotation plant was operated. After the cessation of attempts to float the oxidized minerals, chloride-volatilization experiments were resumed. The highly infusible flotation. tailing from the operation of the flotation mill was used for furnace feed. The first tests made on flotation tailing mixed with 10 per cent. common salt showed -nearly complete lead and gold volatilization but considerably less volatilization of silver than in muffle tests. In attempts to increase the silver extraction, the percentage salt in the furnace feed was varied, and it soon became apparent that the use of smaller percentages of salt raised the fusion temperature of the furnace charge and thus,

Jan 8, 1925

By H. O. HOPMAN

(Canal Zone Meeting, November, 1910.) I. INTRODUCTION. THE substance of this paper was prepared for the Seventh International Congress of Applied Chemistry, held in London, May, 1909, under the title, Some Developments in Blast-Roasting. In the absence of the author, a -short abstract of the paper was read, and the abstract only will appear in the proceedings of the congress. The present paper has been partly rewritten and considerably enlarged by information gained since the original was prepared ; also some illustrations have been added. Blast-roasting' is a generic term for the process of forcing air through finely-divided. metallic sulphide with the object of roasting and agglomerating in a single operation. At first the process was confined to a galena-concentrate ; lime, limestone, or gypsum was added, to serve both as a diluent to keep separate the particles of galena that they might be thoroughly oxidized, and as a flux that the partly-roasted ore might be agglomerated by the formation of some slag. Later it was extended to treat other metallic sulphides. The leading processes were the Huntington-Heberlein and the Savelsberg of Europe, and the Carmichael-Bradford of Australia. In the United States and Canada, the Huntington-Heberlein process has found application in some instances with galena-concentrates, for which it was originally intended; but this class of ore is not often treated alone, hence the process has had to be modified to suit conditions. The Savelsberg process has been transplanted to this country in about its original form. The Carmichael-Bradford is not used at present. The changes called for in the Huntington-Heberlein process to adapt it to the class of lead-bearing ores usually smelted have been the 1 A. S. Dwight, Engineering and Mining Journal, vol. lxxxv., No. 13, p. 649 (Mar. 28, 1908).

Jun 1, 1910

By AIME AIME

HE State of Utah has an area of 84,990 sq. mi., and like other inland states in the West its population, although steadily increasing, is relatively small. The fact that it is a state possessing vast mineral resources is attested by a careful study of statistics which have been compiled by Federal and State investigators. Some idea of the extent of these resources and the degree of development of a particular state or region may be gained by such a study, but in the case of Utah statistics and other available information fail to portray completely the true extent and value of its existing metallic and non-metallic resources. The State is probably more widely known for its production of metallic ores which has placed it in an eminent position among the metal mining states of the Nation.

Jan 1, 1925

Industrial minerals enjoyed a fairly successful year in 1978, despite the sluggish economy, inflation, and environmental restrictions. A glance at US Bureau of Mines statistics shows that, in general, production of industrial minerals increased from + 1% (salt) to as much as 26% (sulfur, other than Frasch or recovered). A few industrial minerals showed a decline; fluorspar production, for example, registered a 23% decrease in 1978 from 1977 due to the closing of three domestic mines. Bromine, natural sodium sulfate, Frasch sulfur, and vermiculite also had production decreases of 2-6% in 1978.

Jan 5, 1979

By B. A. Wilcox

ThERE are several reports in the literature which indicate that both solid-solution hydrogen and hydride precipitates can promote low-temperature em-brittlement of tantalum.1-3 For example, Imgram et al.2 showed that hydrogen additions in the range of 140 to 580 ppm promoted a ductile-to-brittle transition at slightly above room temperature in both wrought and recrystallized tantalum. This contrasts with the observation that tantalum of norma1 purity is very ductile, even at liquid-nitrogen temperature. Imgram et al. also found that hydrogen additions caused a deterioration of notch tensile properties of tantalum. The purpose of this communication is to present some limited evidence that hydrogen can also cause fatigue embrittlement of tantalum. The material used in this investigation was wrought, stress-relieved (1000°C, 1 hr), are-melted tantalum rod (5/8-in. diameter) containing the following impurities in weight percent: 0.005 C, 0.007 02, 0.0005 H2, 0.003 N2, 0.08 Cb, 0.01 W, and 0.01 Fe. Hydrogen charging was done in an atmosphere of flowing dry hydrogen for 3 hr at 600°C, followed by an homogenizing anneal in purified argon for 15 min at 600°C, and cooling in an argon atmosphere. Typical micro-structures of the hydrogen-free and the hydrogen-charged materials are shown in Fig. 1(a) and Fig. 1(b), respectively. Fig. 1(b) shows the appearance of hydride precipitates which, in many cases, formed preferentially parallel to the rod axis. The hydride dispersion was uniform across the diameter of the specimen. The fact that the precipitate was a tantalum hydride was tentatively confirmed by X-ray diffraction on a metallographically prepared surface. After hydrogen charging, chemical analyses by vacuum fusion revealed the hydrogen content to be 0.0295 wt pct. In addition, the oxygen and nitrogen contents were slightly raised to 0.0095 O2 and 0.005 N2.

Jan 1, 1964

By W. L. Saunders

WHEN work was begun in September, 1910, on the rock excavation for the foundation of the gigantic dam at Valhalla, N. Y., which is to convert Kensico lake into an important storage reservoir of the Catskill Aqueduct system, one of the first steps taken by the contractor, H. S. Kerbaugh, Inc., was the development of a quarry to supply the stone needed in the construction work.The importance of a bountiful supply of suitable rock in an accessible location is apparent when it is considered that nearly a million cubic yards of cyclopean masonry will be contained in the completed structure, not to mention dimension and facing stones, concrete blocks, and mass concrete. The dam structure will be over 1800 ft. long and about 170 ft. above the present river bed. However, for a distance of some 800 ft., it will be carried down to solid ledge rock, which will make the finished structure about 300 ft. in maximum height. It will be about 200 ft. thick at the base and directly beneath the coping it will be 28 ft. thick. This dam will raise the reservoir surface 110 ft. above old Kensico lake. The reservoir capacity will be 29,000,000,000 gal.-equal to New York's total needs for over two months. The contract price for this work is nearly $8,000,000 and is second only in amount to the cost, over $12,600,000, of the Ashokan Reservoir work. Fig. 1 is a view of the dam site.

Jan 2, 1914

By A. M. Gaudin

Jan 1, 1962

By Samuel M. Shallcross

The principal function of the Bell limestone mine, of the American Lime & Stone Co., at Bellefonte, Pa., is to supply raw material to the company's modern rotary kiln plant at Bellefonte. Because mining costs are naturally higher than many open quarries with more favorably lying strata, it cannot compete, except to a limited extent, in the markets for road material and fluxing stone. In the broad sense, mining does have an advantage over the average open quarry when the end products are designed for and controlled by process and final inspection for the exacting demands of the industrial and chemical markets. Approximately 80 per cent of the output of the Bell mine is sold in the industrial and chemical markets. And as higher standards are set each year for construction and agricultural work, the remainder of the mine output goes to these two classes. Mining produces more fines than open quarries, and these fines are difficult to market; on the other hand, owing to absence of contaminating clay and impure rock, a greater percentage of the output of a mine is marketable. Because of the great production of fines, rotary kilns for lime burning are necessary when the stone must be mined. In 1921 the American Lime & Stone Co. operated 19 quarries and 72 lime shaft kilns spread over an area of 40 miles between Bellefonte and Altoona, Pa. At that time the lime-production capacity of the 72 kilns amounted to approximately 700 tons per day. After 15 years the company operates three rotary kilns and six shaft kilns, with a combined output of approximately 500 tons of lime per day, concentrated in its single Bellefonte plant (Fig. 1). Its only stone-producing plants are now the limestone mine at Bellefonte and a construction-stone open quarry at Union Furnace, near Tyrone, Pennsylvania. Since the middle of 1922, the management of the American Lime R. Stone Co. has been under the direction and ownership of the Warner Company, of Philadelphia. To the Warner Company's experience, gained through successful operation of lime plants in eastern Pennsylvania for many years, and the successful solution of material-handling problems

Jan 1, 1937

By C. W. Goodale

TOMBSTONE, a name not exactly full of cheerful suggestion, has a great record as a mineral producer and a colorful history as a frontier mining camp. The only practical route to Tombstone in the early 80's was by way of San Francisco and Los Angeles. The Southern Pacific was building across Arizona, and a sleeper was attached to a construction and freight train at Los Angeles, and was trailed slowly across the Colorado Desert to Benson in the San Pedro Valley. Thence one staged 26 miles to Tombstone, which is located near the foot of a range of hills at an altitude of about 4500 ft.

Jan 1, 1925

By J. D. Price, W. M. Bertholf

In preparing a paper on coal washing in Colorado and New Mexico, it is difficult to refrain from entering into a discussion of the historical aspects of this subject, for the story of coal washing in these states goes back well into the last century. This phase of the subject could well make a complete paper in itself, and of necessity this present discussion must be limited to current operations. Therefore, we are taking into consideration only those washing plants which have operated for some period during the years of 1947 and 1948.

Jan 1, 1949

By C. A. LINDBERG

Several new methods have been developed on the Iron Range to remove the material adhering to truck bodies in freezing weather. A machine known as a Gradall, incorporating the features of digging both above and below the horizontal, digging angle of blade control, full revolving, travel almost anywhere, and operated by one man, has proven successful in trials at body cleaning. Several of these units are in use with great saving in box-cleaning costs and improvements in efficiency of the truck operation with full capacity boxes. In addition to their winter use, the same machines have been used for ditching and excavating in the summer with great saving. The latest method of combating this freezing problem is to carry the exhaust from the engine through the body, making use of the tremendous heat that is now being wasted. To do this, the present wood sandwich which is used between the bottom of the box and the wear plate is removed and replaced with angles or channels run lengthwise of the box and spaced to permit gases to flow between or through them and also provide a good sup- port for the wear plate. The channels or angles are cut a little short on each end to form a cross passage that permits the gases to flow through the area. In the front end, openings are made in the wear plate and connect to a manifold created by welding a plate across the whole front of the box, spaced from the original end by the original vertical reinforcing angles at that point. The body being described is for a Euclid truck which is the only truck that has been adapted to this body-heating idea to date. At the rear of the truck, the holes from the cross passage are made in the bottom plate of the body and lead into a triangular-shaped body cross member under the scoop end of the truck.

Jan 1, 1949

By W. WANJUKOW, H. O. Hofman

(New York Meeting, February, 1313.) I. INTRODUCTION. IN the metallurgical treatment of most metallic sulphides it is usually necessary to carry on a roasting-operation. In some cases the raw ore will have to be roasted.; in others the intermediary product, matte, produced in smelting the ore; again, both ore and matte may have to be subjected to oxidation at elevated temperatures. Most metallic sulphides, when given an oxidizing-roast, pass through the state of sulphate before they are converted into oxides. All metallic sulphates are completely decomposed by heat, with the exception of those of lead and bismuth, but the temperatures at which decompositions take place vary with the metals. Some metallic sulphates are converted directly into oxides, others first form basic salts. Alkali-earth sulphates show a behavior similar to that of metallic sulphates, while alkali sulphates do not part with their sulphur trioxide even at elevated roasting-temperatures. The older data on the decomposition of metallic sulphates by beat are only approximations. Thus Kerl 1 gives the order in which metallic sulphates are decomposed with increasing temperatures as (Ag2, Fe, Cu, Zn, Ni, CO, Mn, Pb) SO4. More recent statements give definite temperatures and modify the formerly accepted order of decomposition. But the temperatures given by various observers do not agree. The reasons for this are to be found mainly in the method and manner of carrying out experiments. Four methods have been used: 1. Heating in an evacuated tube; 2, heating in a tube closed at one end, without air-cur-

Sep 1, 1912

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967