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By J. L. Keats

IN THE literature on the elimination of metalloids in basic open-hearth practice, there are a great many heats recorded in which excellent data on changes in slag and metal composition during refining are given, but in almost all of these heats either temperature data or weights and analysis of charge are unrecorded and observations on the physical characteristics of the slag are almost always lacking. With these points in mind, a test heat was made in which as complete as data possible on all the factors that affect the elimination of metalloids were obtained. THE TEST HEAT The test heat was made in a standard 100 ton stationary furnace at the Lackawanna Steel Co., Lackawanna, N. Y. on January 17, 1922. The Charge-Scrap.-The scrap consisted entirely of rail-heat butts, selected from a number of heats made, the week before the test. The average analysis of the scrap was calculated from the analysis of these heats-and from the weight of scrap from each heat. Pig Iron.-Two ladles of pig iron were used in the charge and two samples were taken from each ladle as it was poured into the furnace. These four samples were composited for the average pig-iron sample.

Jan 2, 1926

By John Birkinbine

In the preparation of the paper upon " The Operation of Warwick Furnace, Pennsylvania, from August 27, 1880, to September 1,1885," presented at the Pittsburgh meeting, I purposely refrained from offering theories to explain the peculiarities of furnace operation, on the ground that it was better for those actively engaged in blast-furnace management to present records of operations, than for one more directly interested in blast-furnace engineering and construction to venture upon the sea of speculation as to causes. The manager of an iron-works naturally feels that he knows as much about his particular furnace or furnaces as any one else, and as Mr. Cook, after his close attention to and study of the Warwick furnace, was at that time unwilling to present theories, I felt a disinclination to assume more acumen than the manager.

Jan 1, 1887

By M. H. Shumate

Rope-type haulage has had many applications in the mining and allied industries. Records have indicated favorable results both from a standpoint of efficiency and investment. The Truax-Traer Coal Co. has used some variations of rope haulage at their mines and preparation plants. They have built a system which solves their particular problems, and have an investment which has indicated an annual savings in operating costs. Rope haulage, as applied to the mining industry, goes back many years for both underground and surface mining, or a combination of both. The Truax-Traer Coal Co. has used gravity retarding hoists as well as several variations of rope haulage, including electrical and combinations of both, but each was limited in its use and application by natural conditions and economies of the operation. Several systems of rope haulage equipment are offered by manufacturers today for handling railroad car movement on a limited or continuous basis. The portal and railroad loading facilities of Truax-Traer Coal Co.'s Burning Star Slope mine, located in Jackson County, Ill., were moved in 1960. The old location was abondoned, eliminating 3% miles of underground track haulage. The mine was converted to an all-belt system, and coal is loaded at a new raw coal plant and shipped by railroad cars to a central cleaning plant. The company wanted to operate the surface facilities as efficiently as possible, employing a minimum number of workers, using the latest type railroad car movers. The existing rope haulage facilities at several locations throughout the country were examined and considered for the Slope mine location. The application of each appeared favorable but lacked flexibility, and it was difficult to justify the capital investment. The company decided to investigate the possibility of building a system that would apply to their problem, and have an investment that could be amortized in a relatively short period. SPECIFICATIONS They employed the services of Allen and Garcia Co. of Chicago, Ill. Through combined efforts, a railroad car rope system was designed to specifications as shown in Fig. 1. The Falk Corp. of Milwaukee, Wis. built the hoist to the specifications as shown in Fig. 2. It has an all welded base and pedestals. The all welded drum is not grooved. A single helical gear was used in lieu of herring bone type. A Falk speed reducer, Unit 90Y3-A, is driven by a 25-hp 1800-rpm, 440-V ac type 'C' (high starting torque) drip-proof, Frame 324-U motor. The speed reducer shaft is equipped with a solenoid operated ac spring set shoe brake, operating on a 7-in. diam. brake wheel. The dolly car, shown in Fig. 3, was field constructed, using the trucks and frame of a railroad tank car. Truax-Traer did not alter the frame but added plates and anchors for hoist ropes and frames for 8.5 tons of concrete to be used as ballast on the car. The limit switch operating shoe was also installed and the car coupler latch mechanism overhauled. The hoist rope selected was 1% in. in diam., 6x37 improved plow steel extra flexible, right lay, regular lay, with independent wire rope core, and preformed. Wedge sockets were used to connect rope to the dolly car as shown in Fig. 4. The system employs two 30-in. and three 16-in. diam. sheaves. All are bronze bushed and equipped with grease fittings. Larger sheaves are used for directional change of hoist rope and the smaller ones as snub sheaves to correct fleet angle of rope as it approaches the hoist drum. The Trench lay cable, buried between the two tracks, is used for electrical distribution and controls between hoists and operator's cab. Foundations for the system required 187 cu yards of reinforced concrete using approximately 60 cu yd each at three locations. Four hoists are employed in the system, two for each track. A pair is interconnected electrically and when one operates, moving the cars, the tail hoist idles with brake released. The process is repeated for the reverse direction. A limit switch, mounted in the track near each end of the system, is tripped by the dolly car as it approaches the hoist. The limit switch controls movement in one direction only, protecting the dolly car and establishing positive con-

Jan 1, 1962

By William Fink

THE investigation of the phase relations of high-purity aluminum-base alloys is a part of the fundamental research program of the laboratories of the Aluminum Company of America. The results of a number of binary and ternary systems have previously been published in the transactions of this society. The aluminum end of the binary aluminum-titanium system has been studied. This system has received relatively little attention. To the authors' knowledge, there are two previous papers on this subject. E. van Erckelens1 determined the constitutional diagram reproduced in Fig. 1. .According, to this diagram, the liquids represents the separation of TiAl4 (Ti = 30.7 per cent.). He concluded that this is the composition of the compound, because in his work the eutectic horizontal terminated at 30.7 per cent. titanium and the metallographic examination of a sample of this composition revealed only one phase. According to the constitutional diagram developed by W. Manchot and A. Leber,2 reproduced in Fig. 2 from data given in their article, the liquidus represents the separation of the compound TiAl3 (Ti = 37.2 per cent. ). The composition of the compound was derived in a manner similar to that utilized by van Erckelens. Moreover, Manchot and Leber confirmed the composition of the compound by analysis of the constituent left as a residue after dissolving the alloys in weak sodium hydroxide solution. Although these are the only publications describing the constitution of the system, other investigators have studied the composition of the titanium compound. L. Wöhler3 says that there is a compound TiAl3 which was later confirmed by W. Manchot and P. Richter4 and by

Jan 1, 1931

By M. J. Pearse

The processing of fine particles inevitably produces slimes. These present a dewatering problem, for which gravity thickening provides a partial or preliminary solution. The paper shows the effects of practical factors in carrying out laboratory sizing tests for thickeners. Several methods of determining thickener unit area have been compared for a lightly coagulated phosphate slurry and a highly flocculated kaolin slurry. Practical techniques of mixing and flocculant addition have significant effects on batch settling data. Pulp temperature and cylinder dimensions are very important. Errors in sizing thickeners for highly flocculated slurries by the standard methods are discussed. Such methods are suitable for less compressible slurries, however. Rules of thumb for flocculant selection are given.

Jan 1, 1980

By Albert F. Schneider

The peculiar conditions under which lead and silver ores are now smelted in Salt Lake Valley, Utah, render it advantageous to make slags that are siliceous and carry a high percentage of lime. The ores treated come from Utah, Idaho, Montana, and Nevada; nine-tenths coming from Utah. These ores are siliceous, and contain but little fluxing material; the iron present scarcely sufficing for the sulphur and arsenic. Formerly ores high in iron were furnished from Cottonwood Canons, but this supply is meagre. The ores from Idaho, Montana, and Nevada are high grade galenas, more or less impure. They generally require a large amount of iron for the sulphur, arsenic, and antimony. In the winter and spring of 1880—'81, we were treating at the Germania Works principally Bingham Canon lead ores and silver ores from Tintic. The former contained 15 to 30 per cent. silica, and only 4 to 5 per cent. iron (generally as iron pyrites); they ranged high in lead and low in silver, and carried more or less alumina; the lead was present chiefly as carbonate. The silver ores from Tintic contained sulphides, and ran as high as 80 per cent. silica. We had been running on a slag approximating 40 per cent. FeO, 20 per cent. CaO, 10 per cent. other bases, and 30 per cent. SiO2, which had heretofore been very satisfactory; but with the class of ores then coming in it was of the utmost advantage to use less iron and more lime, especially as the iron ore (50-55 per cent. iron and 5-7 per cent. silica) cost four times as much as the limestone (50-55 per cent. lime, 3-5 per cent. silica). The large amount of alumina in the slag influenced them for the worse; the addition of lime to the charge helped them, and after many experiments regarding the proportion of FeO, CaO, and SiO2, a slag approximating 35 per cent. FeO, 25 per cent. CaO, 5 per cent. other bases, and 35 per cent. SiO2 seemed to answer

Jan 1, 1883

By E. Gybbon Spilsbury

In a paper* read at the last meeting of the Institute, in Scranton, Pa., I referred to the proposed introduction at the Haile gold-mine, South Carolina, of a novel method of chlorination. I have since

Jan 1, 1888

By H. Rumfelt

Surface excavators for mining coal and such non- metallic minerals as quarry stone, gypsum, phosphate and the like have advanced tremendously in the last 50 years, and their advancement has paralleled that of excavators used in the construction industry during the same period. Up to a certain stage, the construction industry led the way with this development and even pioneered in how the equipment was used. Afterwards, however, new mining machinery and related operating techniques progressed along a different path than their construction counterparts because of the different demands of the two industries. The word "stage" as used above quite generally connotes a transition period, possibly of several years' duration, during which mining development followed the construction industry. Later, mining branched out and responded to its own needs. Most readers are familiar with the events which led to the development of the power shovel. The first dredge was recorded as having been used in England in the latter 1700's and was no doubt developed along the lines of some notes written in the late 1400's by Leonardo da Vinci.

Jan 1, 1971

By R. Costantini

Long-distance transportation of solids by hydraulic pipelines holds promise of great economic benefits. In most mineral processing plants today, moving of solids in slurry-form by pipeline is commonplace. Yet in spite of this, the method is slow in being adopted on a broad scale for moving solids over distances of many miles. This is especially surprising in view of the successful realization of two daring ventures in long-distance solids pipelines in this nation within the last five years. One is the 72-mile long, 6-in. diam. pipeline of the American Gilsonite Co. which has been satisfactorily transporting 700 tpd of gilsonite from the mine at Bonanza, Utah, to the processing plant at Grand Junction, Colo., since April 1957. The other is the 108-mile long, 10-in. pipeline of the Pittsburgh Consolidation Coal Co., which has been transporting about 4000 tpd of finely crushed coal from the mine at Cadiz, Ohio, to the Eastlake Power Plant of the Cleveland Electric Illuminating Co. since January 1958.

Jan 8, 1961

By S. F. Turcotte, B. J. Grierson

At the Q. I. T. ilmenite smelter, nine electric furnaces produce titania slag and iron At high power levels, a furnace requires either a slag or an iron tap approximately once an hour, using rail cars as slag receptacles and ladles for iron. The correct scheduling of taps is an important operational tool due to peak power load and operational considerations. Over recent years, large increases in furnace capacity have imposed severe strains on the product handling facilities. This situation results in loss of production when several taps are bunched, because of an in- ability to handle many taps simultaneously. An on-line computer program has been developed to generate schedules for tapping a single furnace. By improved scheduling, this program can en- large the tonnage of each tap and minimize the number of taps, while reducing traffic congestion and unit cost s. Future plans call for extension of this technique to all nine furnaces with addition of a master scheduling program to optimize the overall traffic flow in the smelter aisle.

Jan 1, 1969

[Paragraph No. PREFACE ON ASSAYING I BALANCES AND WEIGHTS 2 Balances required for Assaying 13 How assay Weights are made 3 Assay Weights based on the Centner 18]

Jan 1, 1949

By George M. Fowler, R. E. Illidge

Part I. Developing BY GEORGE M. FOWL INTRODUCTION The Tri-State district comprises an area of about 2000 square miles in southwestern Missouri, southeastern Kansas, and north [ ] eastern Oklahoma. The part that is in and contiguous to Missouri is still sometimes designated as the Joplin district (Fig. I). EARLY OPERATIONS Mining operations in what is now the Tri-State district date from about 1848 and have been continuous to the present. Apparently the first discoveries of ore were made about the same time near the present sites of Joplin, Oronogo, and Granby. Lead minerals were found at grass roots, probably in shattered rock in shallow excavations, then these minerals were followed in shear zones to deeper horizons. The mining of zinc followed. Before 1874, zinc ore was worthless and discarded as waste. According to published records, the total production of lead to that date was 49,000 tons of metal from 70,000 tons of concentrates. PRODUCTION The aggregate ore production from the Tri-State district was recorded at interval

Jan 1, 1943

By B. H. Sage, W. N. Lacey

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By W. N. Lacey, B. H. Sage

The results of an extensive experimental program relating to the effectiveness of gravel screens have been correlated. The factors considered in some detail include gravel size and condition of packing, sand size and size distribution, fluid velocity, fluid viscosity, and thickness and arrangement of grave! screens. Good agreement between calculated values based upon probability considerations and experimental results relating to the influence of the thickness of the gravel screen was obtained. All of these factors are treated in the correlation in order that their influence may be taken into account in ascertaining the characteristics of an effective gravel screen for a particular set of conditions. The details of the experimental program are not given in the present paper but a description of generalized behavior and typical experimental results are recorded in graphic form. Introduction Gravel screens have been placed in water and oil wells for a number of yearsl,2,3 with the dual objective of increasing the productivity and decreasing the entrance of sand into the well bore. An understanding of the factors controlling the effectiveness of gravel screens in this connection is of industrial interest because it will lead to the proper selection of gravel. Some of the fundamental considerations involved in the migration of sand through a coarser body of porous materials were investigated by Coberly and Wagner4 and further experimental work has been carried out by Gumpertz.5 Apparently the pertinent phenomena are somewhat complex and are influenced by many variables. The present paper deals with the prediction of the behavior of gravel screens under the conditions encountered in practice but does not attempt to discuss the experimental methods or results that were obtained as a background and upon which the prediction is based. Influence OF Gravel Screens upon Productivity The use of a gravel screen may increase the productivity of a well by increasing its effective diameter, and this constitutes one of the objectives of its use. The permeability of most gravels and coarse sands that are employed in practice is so large compared to that of the sand in place that relatively little loss in production rate will arise from the use of material fine enough to cause the desired resistance to sand migration. For example, in Fig. I is depicted the approximate variation in the permeability of closely sized spherical gravels under the conditions of packing likely to be encountered in screens. The dotted lines indicate the variation that might be found because of differences in packing. It should be realized that the permeability is not a single-valued function of the average grain diameter but is related to a large number of factors, including the size, the size distribution and the shapes of the particles. However, Fig. I does permit a rough estimation of the permeability of closely sized spherical gravels and shows that the permeability with even the smaller particles is very large compared to that of most petroleum production horizons.

Jan 1, 1942

By D. R. Miller

The use of fully grouted cables for ground reinforcement in underground mining is becoming widespread. Reinforcement design for this application has tended to be empirical although some two- dimensional design techniques have been developed. This paper describes a technique based on a model of the behaviour of cables placed across planes moving in shear. The model is three- dimensional and includes a simple model of the 'dowel' effect which arises from the bending of the cables. The model determines the shear resistance developed at a particular shear displacement assuming joint friction and cable parameters. Using data for twin 15.2mm dim. steel strand cables, and a concept of reinforcement efficiency, the application of the model to design wall support in open stopes is demonstrated. The examples consider the cases where major planar structures are known in location and orientation and where, as is more common is open stope development, mapping has indicated that a distribution of potential shear failure structures may be present. The actual location and orientation of potential shear planes is not known. These two cases highlight the underdesign of reinforcement that may arise if the distribution of orientation of potential shear planes is not considered.

Jan 1, 1984

By A. A. Collins

OF widespread interest to all lead metallurgists is a dross smelting process that will consistently give mattes and speiss of low lead and high copper contents. It is a problem that has intrigued operators through the years. In the past few years, with increased amounts of copper and overcrowded metallurgical furnaces, it has been almost imperative to evolve some method. Experience at El Paso has shown that high copper-to-lead ratios can be consistently attained by use of the new soda process. † Older Methods Three older methods, i.e., 1. Dross plus siliceous ore and limestone. 2. Dross plus one fourth blast-furnace speiss and siliceous ore, 3. Dross plus sulphides and siliceous ore and scrap iron, do not give consistent results and the products are higher in lead and lower in copper than those produced with the soda process. Any radical changes in the blast-furnace drosses will throw any of these older methods into a tailspin. For almost ten years, El Paso used the third method, with varying results. It was noted that as the arsenic and anti- mony contents of the dross increased, the speiss and matte steadily increased in lead and decreased in copper. A dross containing four parts of copper to one part of arsenic was considered to be ideal. At times this balance of copper to arsenic was almost impossible to obtain, especially when handling copper Cottrell dusts, which vary so greatly in copper and arsenic. Custom smelters like El Paso, handling a great variety of dusts, concentrates and ores, are apt to have anywhere from I to 15 pct copper on charge, with a variable in arsenic of from 0.5 to 2 pct. With such conditions, and drosses varying from 12 to 40 pct copper, an operator using the older dross reverberatory practices would find it just about impossible to control the reverberatory operations and to produce a good product low in lead and high in copper. These conditions prevailed at El Paso from the year 1940 to the present. In May 1942 it was decided to experiment with the soda process. The Soda Process After considerable work the soda method was finally evolved to the present state. It has never failed to produce a good product even under the most adverse conditions. It might be well to remember that many men of thought in the smelting industry have at one time or other sugge~ted the removal of all copper, arsenic and antimony from the lead blast-furnace charge as an aid to better metallurgy.

Jan 1, 1949

By AIME

TITANIUM-RICH ilmenite deposits, situated in the Allard Lake area in Quebec some 400 miles down the St. Lawrence River from Quebec City and 28 miles north of Havre St. Pierre on the north shore of the Gulf of St. Lawrence, are undergoing an intensive development program by the joint efforts of the Kennecott Copper Corp. and The New Jersey Zinc Co. Easily accessible ore, amounting to about 125 million long tons and carrying from thirty to forty per cent titanium oxide, has been delimited. Plans are being made for construction of an electric smelter at Sorel, on the south bank of the St. Lawrence midway beween Montreal and Three Rivers, which will produce 650 long tons of high-grade titanium slag and 500 long tons of iron per day from 1500 long tons of ore. Occurrence of ilmenite ore in this area has been known since J. A. Retty reported his geological work in the lower Romaine River area for the Quebec Bureau of Mines in 1941. In this report Dr. Retty mentions the presence of anorthosite rocks, some of which were rich in ilmenite. Claims were staked by several interests but the small showings and complex metallurgy were too formidable for any organization not adequately equipped with capital, metallurgical knowhow, and market outlets. However, Kennecott became interested and through a newly formed Canadian subsidiary, Kennco Explorations Ltd., options were taken up under the direction of A. H. Robertson. An area of 300 square miles was traversed in the summers of 1945 and 1946. During 1946 and 1947 geophysical and diamond-drill prospecting disclosed a num-

Jan 1, 1948

By Charles Morgan

AN increased demand for brown iron ore in the Birmingham district during the past 18 months has caused renewed activity both in prospecting and mining these ores. In recent years the production in Alabama has ranged from 41,559 tons in 1932 to 639,351 tons in 1928. During the last 9 years about 83 per cent of the total brown ore produced in the United States has come from Alabama (Tables 1 and 2). PROSPECTING Two methods of prospecting are used in this district: (1) test pits, (2) churn-drilling. Usually there is certain quite definite information on an area to be prospected; some of the indications are float ore suck as small gravel or small and large boulders known as "dornicks” scattered over the surface, and ore exposed by erosion in gulleys and ravines, which have cut or eroded through the overburden. Often these natural erosions furnish an indication of the thickness of the ore and to some extent of the area of the ore body. Deposits of brown ore are very irregular both in thickness and extent. Deposits are often lens-shaped or long narrow leads, some of which may be parallel and separated from one another by sand, clay or gravel. The bottom-the footwall-is also very irregular. This footwall is usually lime clay-disintegrated limestone, locally called "white horse," which usually is found at a depth of 6 in. to 20 ft. overlying the limestone. At some places sand and gravel is found under the ore instead of clay. No ore is found under the lime clay, although often the ore has sunk or slumped and is found in the upper portion of this clay, as at some of the Sloss workings at Russellville. The origin of these ores has been discussed by Major E. C. Eckel and Dr. E. F. Burchard in U. S. Geological Survey Bulletin 400, and recently the latter has done further work on ores in the Russellville district, of which reports undoubtedly will be published.

Jan 1, 1937

By J. S. Ll. Leach, M. B. Bever

THE system copper-nickel exhibits complete solid and liquid miscibility1 The thermodynamic properties of such a system would not be expected to deviate greatly from ideality. Although the evidence is conflicting, anomalies in the composition dependence of various physical properties of solid copper-nickel alloys suggest that mixing may not be ideal.' From measurements of the Hall coefficient it has been concluded that clustering occurs in these alloys. ' Considerations involving the phase diagram of the ternary system copper-nickel-chromium have led Mei-jering3 to predict a positive heat of formation for solid copper-nickel alloys. An electrochemical investigation of the activity of nickel in copper-nickel alloys showed unexpectedly large positive deviations from ideality.4 wagner5 has proposed that if the entropy can be considered ideal, these measurements would yield the following equation for the heat of mixing at 700°C H" = 3380 x,vl (l-xVi) cal per g atom [I1 The heat of formation at 722°C of solid copper-nickel alloys of the equiatomic composition has been measured in a reaction calorimeter as 540 cal per g atom. This note reports calorimetric measurements of the heat effects on dissolution of some copper-nickel ndon: in tin. These measurements were preliminary to a larger investigation, which was later discontinued. From them the heats of formation of the alloys can be calculated, if certain assumptions are

Jan 1, 1960

By E. C. Barfield, D. G. McCarty

Two-dimensional analyses offer considerable promise in providing the basic information required to effect more precise control of petroleum reservoir performance. This paper describes a method for conducting some engineering analyses of this type using a high-qreed digital computer. The general approach is to (I) develop a representative numerical model of the reservoir and (2) employ a suitable numerical technique to solve the basic equation of flow and to develop the required engineering information for the particular case represented by the model. This technique has been used to calculate pattern performance in connection with several field projects involving water injection into oil reservoirs. This type of analysis involves sequentially (I) calculating the pres-' sure distribution in the reservoir and (2) tracking the progress of the interface between the displaced and displacing fluids in a step-wise manner to provide a depletion history of the operation. The particular analysis presented in this discussion is subject to the restriction that the mobility of the displaced and displacing fluids be equal and assumes that the fluids are incompressible and that gravity and capillary pressure do not affect the shape of the flood pattern. Complete two-dimensional .flexibility is maintained with regard to definition of reservoir rock and fluid characteristics, placement of physical restrains and boundary conditions, investigation of flow characteristics in the reservoir, and movement of the displaced and displacing fluid interface. The results of these studies indicate that the highspeed digital computer is well suited for conducting reservoir performance studies in two-space dimensions and that dependable numerical techniques are available for making such analyses. INTRODUCTION One of the problems facing petroleum engineers is that of providing more precise engineering control over reservoir operations at all stages during the depletion cycle. The most direct approach to this problem is to simulate the reservoir with some type of physical or mathematical model and use the information developed from the behavior of the prototype to predict the performance of the actual reservoir. This principle is, of course, not new, and a variety of simulation techniques have been developed to provide information on the behavior of oil and gas reservoirs. One straightforward refinement of present reservoir analysis techniques is the progress from one-dimensional reservoir models to those where the reservoir can be represented in two- and three-space dimensions. Multidimensional reservoir analyses are desired in order to show not only what is happening in the reservoir but in addition to show where in the reservoir the various phenomena of interest are occurring. Thus far, two-dimensional analyses have been confined predominantly to potentiometric and electrolytic model studies. However, when large numbers of wells are involved and where large-scale models are required, such problems become very tedious and instrumentation problems become acute." It is possible through use of numerical methods and general purpose digital computers to avoid many of the instrumentation difficulties and to relax some of the restrictions of previous techniques. The purpose of this paper is to discuss some recent experiences with the use of high-speed digital computers for predicting pattern performance in fluid injection operations and to describe the numerical procedures which have been used for making such analyses. THE NUMERICAL MODEL The problem of representing the reservoir with an appropriate numerical model is composed of at least two important considerations. The first requires that an adequate description of the reservoir mechanism be formulated in the form of the basic differential equation describing the process. The second consideration is definition of the physical characteristics of the reservoir. The latter requires that representative basic data be obtained, examined, and interpreted to provide sufficient detailed definition of the pertinent physical properties throughout the system. The Differential Equation One of the basic assumptions made for the purpose of performing the two-dimensional studies being dis-