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By C. L. Sollenberger, Will Mitchell, Ford F. Miskell

Heat treatment of ore prior to comminution reduces power requirements for grinding, reduces grinding media wear, and improves recovery of iron values from a typical Minnesota magnetic taconite. Test data demonstrating this, as well as an analysis of the economics of commercial application of the technique, are presented. THE taconites in general are hard, tough ores, difficult to grind. Liberation of iron mineral constituents usually is accomplished by grinding the ore through at least 100 mesh, and often it has been found necessary to grind substantially through 325 mesh to achieve satisfactory recovery and grade in the concentration process. Because of the fineness of grind required and the enormous tonnages of material contemplated for treatment in the future, costs resulting from grinding media wear and power consumption, together with capital investment required for comminution, approach astronomical figures. Economy in any one of these elements per ton of material ground could very well reflect a considerable saving to the ferrous industry in yearly costs. With this in mind, the Research Laboratories of Allis-Chalmers Manufacturing Co. have launched a program to discover means of effecting this economy. The initial phase of the work as described here deals with a heat treatment of crushed raw ore, followed by thermal shock in cooling, for the preparation of rod mill feed. Several investigators1-" ave noted an improvement in the grindabilities of ores treated in this manner. One investigator2 subjected low grade iron ores to heat treatment in an electric furnace. Basing his conclusions on screen analyses of crushed products, he observed that treated ore was more easily crushed than the untreated. He reported that observation of the treated and untreated ore through a microscope revealed cracks following the grain boundaries in treated ore, whereas no cracks were present in untreated ore. However, few if any have quantified the improvement in terms of total hp hours saved, reduction of wear of grinding media, or reduction of capital costs of grinding equipment involved. By means of Bond rod mill and ball mill grindabilitiesh nd by comparative wear tests, the conditions maintained during this investigation have been definitely evaluated. Heat treatment experiments have been made on a batch scale in a muffle furnace, followed by continuous scale experiments in a rotary kiln under various conditions of temperature, atmosphere, retention time, and quenching to determine the combination that would give the greatest improvement in the grindability of a taconite without affecting adversely the magnetic susceptibility of the magnetite. From these data, relative costs have been calculated for grinding both untreated and heat- treated ore on a basis of plant capacity of 120 tons per hour. Heat requirements for a rotary kiln, as well as the kiln capacity required for the treatment, have been estimated. For these tests 50 tons of ore were obtained from the Aurora mine of the Erie Mining Co., Hibbing, Minn. The ore was reported7 to have been selected from the magnetic portion of the lower chert horizons. An average chemical analysis of' this portion is shown in Table I and an approximate mineralogi-cal analysis is shown in Table 11. No attempt was made to differentiate between the various silicates because the compositions vary widely on the different horizons and depend on the degree of oxidation. Minnesotite, however, is the predominant silicate. The siderite grains were dispersed throughout the ore but were essentially associated with the rock-forming minerals. In a series of preliminary tests in which batches of —6 mesh ore were heat-treated in a muffle fur-

Jan 1, 1953

By John Griffen

THE distinguishing principle of the Tromp process is the use of a medium in the bath which is not stable, i.e., the solids will settle and the density of the medium increases with depth. A medium of uniform density can most easily be effected by agitation or by means which increase the viscosity of the medium. Either of these works against the sharpness of separation of coal from its impurities. The Tromp process grinds the medium solids to relative coarseness, allows them to settle downward in the bath without hindrance, and introduces horizontal currents of medium at intermediate levels between top and bottom of the bath. This prevents any accumulation of particles denser than the upper layer of the medium from which the clean coal is conveyed away or an accumulation of particles lighter than the bottom layer or medium whence the refuse is removed. In a relatively shallow bath making a two-product separation, the intermediate horizontal currents sweep these intermediate gravity materials away to be discharged with the refuse removed by the conveyor. Such a system provides a number of advantages. The gravity of separation can be changed simply by changing the density of the medium without changing particle size of medium solids or other conditions, as would be necessary with a system requiring uniform or stable density throughout the bath. Some installations in Europe separate at 1.40 sp gr on one shift, producing a superclean coal, and on the next shift reclean refuse from dry cleaning units and effect a separation at 1.80 sp gr. Medium solids may be much coarser in size consist, which reduces the viscosity of the medium and promotes its fluidity and in turn the sharpness of separation. Coarser medium solids with a more rapid settling rate are much more easily recoverable from the dilute medium rinsed from the products. The Tromp process is not limited to the use of medium solids having magnetic properties. Instal-

Jan 1, 1953

By J. B. Macelwane

Historically whenever application of scientific results to a new problem required the special experimental background, the economic outlook and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering based on the professional requirement grew up in the engineering colleges. This is precisely what is happening now in geophysical engineering. THE Mineral Industry Education Division of AIME has long been interested in geophysical education. Organized in 1938, a Committee on Geophysical Education presented a number of reports in succeeding years. The AIME is an engineering society; hence it might be expected that the interest of the Mineral Industry Education Division would have centered about the relation of courses in geophysics to engineering education. However, this was not the case. The burden of the discussion held under the auspices of the Committee on Geophysical Education bore on geophysics in general and particularly on its relation to geology. In the decade that has passed since those meetings much water has flowed under the bridge. Not only have the geophysical sciences developed at an extraordinarily rapid rate but the practical importance and the range of their applications have spread in ever widening circles and have even assumed a very prominent place in research programs of the military, the Army, the Navy and, particularly, the Geophysical Research Directorate of the Air Force at Cambridge, Mass. So enormously have the geophysical sciences as such grown in scope and in degree of specialization that no one man in a lifetime of study can hope to master the theoretical and experimental complexities or even to follow intelligently in the published literature all the varied accomplishments of basic research in these fields. As in the other sciences, most of the results of geophysical research have potential economic value and are being applied to a wider and wider range of human needs. Here we see a parallel with the older sciences and their relation to engineering. Whenever the applications of scientific results required the special experimental background, the economic outlook, and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering grew up in the colleges and universities. In the words of the "Report of the Committee on Adequacy and Standards of Engineering Education" in the January 1952 number of the Journal of Engineering Education: "Engineering education in America was not developed after a preconceived plan. It evolved in parallel with the needs of a growing country, a country engaged in the development of a vast industrialization. From the first it filled a practical need, and its design emanated largely from an evaluation of the professional requirement." The advent of the railroad created a need for scientifically trained engineers and the response was the curriculum in civil engineering. The development of steam power created the demand for a curriculum in mechanical engineering. Neither of these types of engineers was trained to cope with the requirements of electrical power, and so there came to be a curriculum in electrical engineering. The advent of radio communication and of electronics during the first World War and in the years that followed resulted in the establishment of electronics engineering, sometimes within the curriculum in electrical engineering and sometimes independent of it. The complexities of industrial management have created an ever increasing demand for industrial engineers and the consequent building up of a curriculum in industrial engineering. The wide industrial application of chemical processes required a type of engineer whose background was training in chemistry but who was able to design processes and plants on an industrial scale; hence we have the curriculum in chemical engineering. The advent of the airplane created an entirely new set of problems which were solved by the training of aeronautical engineers. Many of these have called for more and more science and mathematics. Such was the history of the older engineer-

Jan 1, 1953

By Alan Stanley

THE MacIntyre Development of National Lead Co. is located at Tahawus, N. Y., in the heart of the Adirondack Mountains. Operations involve the mining and concentrating of a titaniferous iron ore to produce ilmenite and magnetite concentrates. A general description of the operation and metallurgy has been given by Frank R. Milliken.' Pigment plant production demands that the MacIntyre mill produce a 44.7 pct TiO, ilmenite concentrate. To achieve the required ilmenite grade and tonnage it is important that the table concentrate grade be closely controlled. Unfortunately, however, the titaniferous orebody which feeds the MacIntyre mill is not uniform. Ore dressing characteristics vary from one end of the orebody to the other, and from • one level to the next. The changeable nature of the mill feed precludes a single adjustment of the equipment for long periods of time. Thus the operators must constantly watch the equipment to insure a uniform concentrate from the fine and coarse tables and Wetherills, or dry magnetic separators. Chemical assaying of mill products requires about 4 hr from the time the sample is taken until assay results are obtained, and this is available only on a two-shift basis. The ore may change rapidly, even several times during a shift, so that assay results lose most of their control value by the time they are reported to the mill operating crew. Members of the crew have therefore tried to evaluate the table and Wetherill concentrate by visual inspection, since through long experience the shift operators, under most circumstances, can gage closely the grade of the mill products. However, there are times when the physical nature of the ore is radically different from normal. Under these conditions visual inspection is of no value, and at such times final ilmenite as low as 43 pct TiO, has been produced and shipped before the assay results have been received. The specific gravity method of assaying for TiO, has been attempted to eliminate the shipping of ilmenite below normal grade as well as to help control day to day and hour to hour mill production. Table I shows the minerals found in the MacIntyre ore along with their average weight proportions and specific gravities. The first two products considered for the specific gravity method were fine and coarse table concentrates. It was reasoned that these products were essentially ilmenite with the higher specific gravity gangue minerals. Since they were always produced the same way, and the desired grade of TiO, was always constant, the specific gravity of these materials would increase or decrease as the amount of ilmenite increased or decreased. Thus for table concentrates which assayed 40 pct TiOz a constant gravity would invariably be obtained, and as the TiO, value changed the specific gravity would change in direct proportion. The third product considered was Wetherill ilmenite. It was assumed that a desired grade of 44.7 pct Ti02 would also always contain the same amount and type of gangue minerals along with the ilmenite, and thus would always have the same specific gravity. As the TiO, value of the ilmenite concentrate changed so would its specific gravity. Dr. Kenneth Vincent, chief metallurgist of the Baroid Division of National Lead Co. at Magnet Grove, Ark., ran specific gravity tests on 17 samples of the desired products. The lowest specific gravity reading assayed the lowest in TiO, and as the specific gravity increased the trend was for the TiO, assay to increase, see Fig. 1. Since these results warranted further investigation, a 500-g capacity Torsion balance and 250 ml Le Chatelier specific gravity bottles were obtained. Shift samples of fine table concentrate, coarse table concentrate, and final ilmenite were tested. Each sample was split and 85 g weighed on the Torsion balance. The Le Chatelier bottle was filled with water to a zero mark. To avoid wetting the neck of the bottle it was found necessary to do this

Jan 1, 1953

By J. B. Macelwane

Historically whenever application of scientific results to a new problem required the special experimental background, the economic outlook and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering based on the professional requirement grew up in the engineering colleges. This is precisely what is happening now in geophysical engineering. THE Mineral Industry Education Division of AIME has long been interested in geophysical education. Organized in 1938, a Committee on Geophysical Education presented a number of reports in succeeding years. The AIME is an engineering society; hence it might be expected that the interest of the Mineral Industry Education Division would have centered about the relation of courses in geophysics to engineering education. However, this was not the case. The burden of the discussion held under the auspices of the Committee on Geophysical Education bore on geophysics in general and particularly on its relation to geology. In the decade that has passed since those meetings much water has flowed under the bridge. Not only have the geophysical sciences developed at an extraordinarily rapid rate but the practical importance and the range of their applications have spread in ever widening circles and have even assumed a very prominent place in research programs of the military, the Army, the Navy and, particularly, the Geophysical Research Directorate of the Air Force at Cambridge, Mass. So enormously have the geophysical sciences as such grown in scope and in degree of specialization that no one man in a lifetime of study can hope to master the theoretical and experimental complexities or even to follow intelligently in the published literature all the varied accomplishments of basic research in these fields. As in the other sciences, most of the results of geophysical research have potential economic value and are being applied to a wider and wider range of human needs. Here we see a parallel with the older sciences and their relation to engineering. Whenever the applications of scientific results required the special experimental background, the economic outlook, and the practical knowledge characteristic of the engineer, a curriculum in that type of engineering grew up in the colleges and universities. In the words of the "Report of the Committee on Adequacy and Standards of Engineering Education" in the January 1952 number of the Journal of Engineering Education: "Engineering education in America was not developed after a preconceived plan. It evolved in parallel with the needs of a growing country, a country engaged in the development of a vast industrialization. From the first it filled a practical need, and its design emanated largely from an evaluation of the professional requirement." The advent of the railroad created a need for scientifically trained engineers and the response was the curriculum in civil engineering. The development of steam power created the demand for a curriculum in mechanical engineering. Neither of these types of engineers was trained to cope with the requirements of electrical power, and so there came to be a curriculum in electrical engineering. The advent of radio communication and of electronics during the first World War and in the years that followed resulted in the establishment of electronics engineering, sometimes within the curriculum in electrical engineering and sometimes independent of it. The complexities of industrial management have created an ever increasing demand for industrial engineers and the consequent building up of a curriculum in industrial engineering. The wide industrial application of chemical processes required a type of engineer whose background was training in chemistry but who was able to design processes and plants on an industrial scale; hence we have the curriculum in chemical engineering. The advent of the airplane created an entirely new set of problems which were solved by the training of aeronautical engineers. Many of these have called for more and more science and mathematics. Such was the history of the older engineer-

Jan 1, 1953

By D. O. Wyble, L. O. Bacon

THERE has been considerable speculation among mining geologists and mining men in general as to the relative merits of gravity methods in iron-ore exploration. Most of the investigations which have been carried out in recent years have been done by mining companies, and few if any of the results have been published. Three gravity surveys have been made in the Iron River-Crystal Falls area,' " one by the U. S. Bureau of Mines, with inconclusive results, and the other two by Radar Exploration Co. for the Cleveland-Cliffs and the M. A. Hanna companies, with results not known to the writers. Both the last-mentioned surveys were detailed investigations, the stations being spaced as close as 10 ft along traverses,' and were made to determine the feasibility of locating iron ore by gravitational methods. Because of the presence of a large body of ore already extensively drilled, Dr. Harold L. James of the U. S. Geological Survey, Iron River, Mich., suggested that a further test of gravitational methods of exploration be made in the Round Lake area of Iron County, see Figs. 1 and 2. This survey indicated a considerable regional gradient and led to a study of the surrounding gravity field and its relation to the major structural features of the syncline within which the iron formation lies. The southwestern part of Iron County presents a series of hills and hollows elongated in a roughly north-south direction. The bedrock topography is of pre-glacial origin. Relief is moderate; a maximum elevation difference of approximately 350 ft was observed during the survey. Major drainage is dendritic with the larger streams: the Brule to the south, the Paint to the north, and the Iron in the central part. Hills are thickly grown with hard- woods, and lowland areas, not under cultivation, are usually covered by second-growth softwoods. The area covered in this paper includes the southern half of Iron County, Mich., with a deep synclinal basin occupying the central part of the area, and the southeast corner of Gogebic County, immediately to the west of Iron County. The upper Huronian iron formation, slates, and graywackes which form the synclinal basin rest upon a greenstone basement. The basin has not been completely outlined by exposures, drill records or other means, as outcrops are scarce and the thick mantle of glacial drift makes geological investigations extremely difficult. Glacial drift varies in depth up to 300 ft or more. The drift is usually thickest under the hills and is thinnest in the depressions and along drainage courses where most of the bedrock exposures occur. The area over which gravity investigations were made is almost, entirely covered by glacial material. Bedrock of the basin consists of a complexly folded series of iron formation, slates, and graywackes. One of the series of slates has a high magnetic susceptibility due to the fine-grained magnetite it contains. This formation can be detected readily. by magnetic methods and provides a marker horizon which can be easily followed. The magnetic slates are stratigraphically above the iron formation, and much of the geological interpretation of the area is based upon the magnetic anomalies they produce.

Jan 1, 1953

By Leslie W. Austen

ROTARY kiln operators will agree that some of the most severe conditions a refractory must stand occur in the hot zone of a kiln burning Portland cement, dead burn dolomite, magnesite, peri-clase, and similar materials. Frequently the operator is faced with factors beyond his control which drastically shorten the life of refractories. Shutdown due to mechanical failure can be serious if the period is of sufficiently long duration to cause the dropping of coating or the loosening of the lining. A change in slurry can affect the coating and cause ring buildup. A change in type of fuel and its effect upon the flame can cause a shift in location of the hottest zone. Weekend shutdowns or any other interruption can cause the operator trouble and may damage the refractories, since stopping and starting a rotary kiln is certainly more difficult than stopping and starting a motor. Some operators have tried to set an estimate of damage for each shutdown in equivalent days of running time. Conditions affecting the refractory may be roughly grouped in four classes: chemical attack, mechanical stress, thermal shock, and abrasion. Chemical Attack: The drive to obtain maximum production through a kiln demands maximum operating temperatures, temperatures which are limited more by the ringing up or melting of the clinker. This can cause interface temperatures at the junction of coating and refractory which require the use of a basic kiln block to withstand the chemical attack. Chemical changes take place within the refractory itself, especially in chemically bonded or unburned kiln blocks. These changes cause the formation of the ceramic or burned bond. Migrating liquids or fluxes from the kiln charge have an effect within the refractory and lead to mineral or glass formation. The alkalies, sodium and potassium, migrate into the refractory as silicates, chlorides, sulphates or other salts. They may move under capillary action or may be caused to move by volatilization with condensation in the cooler portion. Mechanical Stress: Concentrated stress may be caused by several factors or combinations thereof. I—The rings of refractories must be kept tight and rigid within the kiln, and this alone demands considerable force to hold the blocks in place. So that the force will not be concentrated, the blocks should fit the circle as perfectly as possible, with the faces in contact overall. 2—As the kiln is heated, thermal expansion takes place at the hot end of the kiln block. Since this disturbs the plane face it too can cause a concentrated stress at the two ends of the block, and shearing stress can be set up within the brick itself because of the difference in expansion between the two ends. 3—If a lining becomes loose and moves in the shell very severe stress can be set up, and as the kiln rotates this load changes and gives the effect of repeated loading. Permanent expansion of the refractory can also cause severe loading. 4—Not least important, flexing of the kiln is frequently the cause of concentrated stresses. Thermal Shock: Thermal shock, the result of heating and cooling too rapidly, occurs on starting and stopping or when a large patch of coating drops, exposing the bricks. Again, its destructive effect is often the result of phase change, liquid to solid or the reverse; dense refractories loaded with glass-forming impurities are particularly susceptible. Thermal shock is a. problem with refractories set in the wall or roof of a stationary furnace, and becomes even more serious in a rotary kiln, the tendency to spa11 being magnified with movement and concentration of stress. Uniform rate of feed and loading insures both better coating and a more uniform stress. Abrasion: If the refractories do not take a coating, abrasion can become a most destructive factor. Movement of the lining in shell or movement of loose blocks causes abrasion, which is also most destructive if the refractories do not take a coating. An analysis of the problem of basic lining for the hot zone reveals, therefore, a number of desirable characteristics: high refractoriness, basic chemical reaction, resistance to spalling, good strength at all stages, ability to take coating, true sizing, volume stability, and abrasion resistance. Increased demand

Jan 1, 1953

By J. R. Lewis, J. H. Hamilton, V. D. Hanson, K. W. Heinlein, J. M.194-000-000-006 Vonfeld, J. P. Denny

TWO overfeed drum-type separators using a suspension of magnetite in water as the separating medium have been installed in the Champion NO. 1 preparation plant of the Pittsburgh Coal Co., Division of the Pittsburgh Consolidation Coal Company. A simplified flow diagram of the Champion No. 1 coarse coal circuit is shown in Fig. 1. A railroad car rotary dump, capable of handling 20 cars per hr, discharges the coal into a hopper. Coal is fed from the hopper of the rotary dump to a 60-in. belt conveyor by two reciprocating pan-type feeders. The belt conveyor feeds the run of mine coal onto the main raw coal screen. The first deck is fitted with 3 in. round hole perforated plate which removes the 3x0-in. coal. The second deck of the screen is equipped with 6-in. lip screens which separate the remaining coal into +6 in. and 6x3 in. The +6 in. coal is transferred to a shaking picking table and then discharged onto the loading boom. The 6x3-in. coal is fed to the No. 2 dense medium vessel for cleaning. The clean coal from this unit flows to a vibrating screen where the medium is removed and the coal sized into 6x4 in. and 4x3 in. The 6x4-in. coal is transferred to the loading booms and the 4x3-in. is conveyed to the clean coal classifying screens to remove degradation. The 3x0-in. raw coal is blended in a system composed of three storage bins having a total capacity of 400 tons. From these bins the coal is fed onto a 48-in. flight conveyor by three reciprocating feeders. This flight conveyor delivers the coal to the Rheo plant. The 3x0-in. coal is then cleaned in two 48-in. Rheolaveur launders each equipped with two Rheo boxes. The first set of boxes removes a primary refuse and the second set produces a middling product which is recirculated in the launders. The cleaned coal and water overflows from the primary launders to two sizing and dewatering shaker screens where the water and — -in. coal are removed for further cleaning in the Rheo fine coal plant. The 3x3h-in. clean coal is combined with the 4x3-in. coal from the No. 2 vessel, sized into 4x2 in., 2x1 34 in., and 1'/4x in., then sent to the loading booms. The 3x0-in. refuse from the primary launders is normally fed to the No. 1 dense medium circuit, but any portion or all of this material can, as an alternate, be processed in the Rheo rewash launder. The primary refuse when fed to the dense medium circuit is screened into YSXO which is cleaned in the fine coal plant and 3x for cleaning in the No. 1 vessel. The clean coal from this vessel is passed over a vibrating drainage and rinse screen, then sluiced to the rewash sizing shaker where it is dewatered and sized for loading. The installation of a pilot plant separating vessel using a suspension of magnetite in water was pro-

Jan 1, 1953

By Strathmore R. B. Cooke, Thomas E. Bam

The paper discusses the mineralogy, structure, and strength of magnetite pellets fired in air and in a neutral atmosphere at various temperatures. The information obtained from this investigation is used to explain the origin of the structures occurring in pellets produced by pilot-plant operation. MUCH experimental work has been performed on i-VL the mechanism of agglomeration and pelletiz-ing of moist ore and concentrates and on the process of firing agglomerates, but except for the work of Tigerschiold and Ilmonil much of the published information is empirical, and the literature contains no information concerning the structure of fired pellets. Results of a preliminary study of the micro-structures occurring in pellets produced both in the laboratory and on a pilot-plant scale are presented in this paper. Most of the results were obtained from pellets prepared from Mesabi magnetic taconite, but through the courtesy of the staffs of the Minnesota Mines Experiment Station and the Bethlehem Steel Co., fired pellets produced from limonite and hematite ores and from Lebanon magnetite have also been examined. The work has been restricted almost entirely to pellets produced without additives, the exceptions being those in which coal was added to the filter cake before rolling. Schwartz has described the microstructures occurring in ore sinters produced under reducing conditions.' Many of the structures and constituents he describes are common to fired pellets, but the constituents normally occur in markedly different proportions. His statement that "in all satisfactory sinter the amount of hematite is small, perhaps not over 2 or 3 per cent" is inapplicable to pellets produced by pilot plant operation or by any process in which air is not deliberately excluded. Pilot plant pellets contain over 90 pct by weight of hematite, and those produced in the smaller furnaces of the Minnesota Mines Experiment Station contain more than 80 pct of that constituent. Preparation of Specimens It is difficult to examine unfired pellets microscopically because of their insufficient coherency to withstand sectioning and polishing. Fired pellets sometimes lack coherency and frequently contain holes which are troublesome during polishing. Impregnation of both air-dried and fired pellets is readily accomplished by the use of methyl metha-crylate monomer." The dry pellets are covered in a test tube with excess monomer, to which a small amount of accelerator has been added. When the test tube is placed in a cooling bath and evacuated with an aspirator, most of the entrapped air is removed, and disruption of weak pellets by boiling of the monomer is reduced to a minimum. Polymerization is then effected by immersion of the test tube in a water-bath at about 45"C, this temperature being held for 4 or 5 days. The test tube may then be broken away from the solidified mass and the pellets sectioned by a carborundum wheel or a diamond saw. Where time is important, impregnation is carried out at a higher temperature by Meyer's method.' Air-dried pellets must be impregnated with especial care; otherwise swelling occurs and the solids are displaced. It is more important to be certain that the monomer forms a reasonably complete network throughout the specimen than that all entrained air is removed, and for this reason the vacuum technique may be omitted. Impregnated agglomerated products and pellets are extremely coherent, section well, and may be polished either by hand or by machine. Hand polishing is not satisfactory for the examination of conditions existing at the boundaries of grains, and for this machine polishing must be used. The Graton-Vanderwilt machine gives excellent results, provided that pressure on the specimen is considerably in excess of that recommended by the manufacturer. Mineralogy of Fired Pellets Only two opaque iron minerals, magnetite and hematite, have been recognized in pellets. The complete identity of, these artificial minerals with their corresponding natural counterparts is shown by their mineralographic characteristics and their X-ray structures. Wiistite has not been found. Slag is the most common transparent constituent of fired pellets. Occasionally conditions have been appropriate for the crystallization of fayalite from the slag, and at other times another crystalline sil-

Jan 1, 1953

By Adam L. Wesner, A. C. Richardson

This paper describes the development of a continuous float-and-sink process to produce coal low enough in ash content to be suitable for production of electrodes. The cleaned coal had a combined iron and silicon content of 0.239 pct. The efficiency of recovery was 84 pct. DURING World War I1 the demand for electrode carbon was greater than could be met by the supply of petroleum coke available for this use. It was believed that coke made from an extremely low-ash coal might be a suitable substitute for petroleum coke. Requirements for electrode carbon to be used for the production of aluminum are that the silicon plus iron content shall be not more than 0.14 pct of the coke. However, during the period when petroleum coke was in short supply, it appeared that relaxations of the specifications might be allowed to permit 0.4 pct iron plus silicon in the coke. For this work, the specifications were that the coal should contain less than 1 pct of ash, and the combined iron and silicon content of the coal should not exceed 0.28 pct. Heavy-liquid separations made on a number of coals showed that if certain size fractions of some coals Were separated at low specific gravities the resulting float products would meet the required specifications. The objective of this work was to develop a continuous, commercially feasible process for producing low-ash coal. After consideration of various processes, the method chosen was a float-and-sink separation using a solution of calcium chloride as the separating medium. Eagle Seam coal was used for the experiments. The —10 +35 mesh fraction was found to be the most promising feed for producing the low-ash content coal. A batch of 30 tons of — --in. coal was screened at 10 and 35 mesh; the yield of —10 +35 mesh was 20 pct of the feed. This fraction comprised the feed for the separation tests. In spite of the fact that this portion was screened a second time at 35 mesh, the coal still contained 16 pct that was finer than 35 mesh. Three-fourths of the undersize was in the —35 +48 mesh range. A representative portion of the —10 +35 mesh fraction was subjected to batch float-and-sink separations to determine the best gravity to be used in the continuous tests to obtain a high recovery of low-ash content coal. The heavy liquid used was a mixture of carbon tetrachloride and benzene which assured complete wetting of all of the particles. As usual in batch separations, adequate time was allowed for each separation so that even the near gravity particles had ample time to separate. The separations were made at increments of 0.01 sp gr from 1.25 to 1.28 and also at 1.32 and 1.59. Each specific-gravity increment was assayed for ash content. From these data it was concluded that 1.27 sp gr was best for the continuous separation of the coal. The products from the batch separation were composited into float 1.27 and sink 1.27 sp-gr fractions; these were assayed for ash, iron, and silicon. Table I shows the results of the batch separations. The composite float 1.27 fraction contained 66.04 pct of the total weight, and had an analysis of 0.79 pct ash, 0.073 pct iron, and 0.112 pct silicon, or 0.185 pct iron and silicon combined. These data are indicative of the results possible if a perfect separation is made at 1.27 sp gr under static conditions. Inasmuch as the method under investigation is a dynamic system these results could not be obtained. It remained to be determined, however, just how close to the theoretical results the actual continuous separation would be.

Jan 1, 1953

By Adrian E. Ross

Diamond drilling through caving formations at depths greater than ZOO0 ft has long presented serious difficulty, generally solved either by casing or cementing. Casing is permitted only when the resulting smaller hole is acceptable, and cementing is frequently a problem at depth. A new method that injects cement under pressure at the desired location is an aid in diamond drilling deep holes. DRILLING through caving formations in diamond drill holes at depths greater than 2000 ft has long been a serious problem. These caving formations are normally passed only by casing the hole or by cementing the hole. Casing the hole is possible only when a resulting smaller hole is acceptable. In as much as only a limited number of reductions are economically practical, cementing is frequently considered the only method suitable for solving these problems. Cementing either by pumping a slurry into the hole or by dropping cylinders containing cement has proved satisfactory on holes under 2000 ft. In holes substantially deeper than 2000 ft these methods are not satisfactory, since during the pump- ing process cement separates out, whereas cylinders usually break before the bottom of the hole is reached. A new procedure, the injector method, apparently solves these problems.* With this method, cement is lowered in the hole in a cylinder, the cement being

Jan 1, 1953

Jan 1, 1953

Jan 1, 1953

By J. A. Barr, R. B. Burt, I. S. Tillotson

THE pumping of solids in water suspension is an important part of many metallurgical and mining operations. In most cases, it is still in the rule of thumb category for which no universal formula has been developed, and much research is needed. Because of the limited and incomplete data available, this article may be classed as an experience paper, which is presented with the hope that some contribution will be made toward the development of the so-called universal formula. This formula, if and when developed, may be evolved from several factors, many of which are not now available for general application. The designing engineer is interested in obtaining accurate forecasts on: 1—the minimum velocities needed to prevent choke-ups in the pipeline, which in turn dictates pipe sizes, 2—power required for pumping, 3—pump selection. The basic factors for a given problem will include: 1—weight per unit of time of solids to be handled, 2—specific gravity of solids, for calculation of volume, friction and power, 3—screen analysis of solids with the colloidal acting, i.e., the slime fraction, a very important factor, 4— shape of particle or some means of determining a friction constant, 5—effects of percentage of solids, 6—development of a viscosity factor to be used in the overall calculations, 7—calculation of the lower limits of pipeline velocities permissible, 8—calculation of total head, pump horsepower, and 9—setting up of pump specifications. In certain limited cases horsepower and total heads and minimum velocities may be computed and a suitable pump selected from basic data, but in many cases, as in mining of Florida pebble phosphate, experience rather than a hydraulic formula still should be used as a basis of selection. Pumping Florida Pebble Matrix Pumping at the Noralyn mine of International Minerals and Chemical Corp. will be used as an example. Other areas will vary as to the characteristics of the matrix, especially the slime content. A typical screen analysis of this matrix is: +14 mesh, pebble size,* 2.1 pct; —14 +35 mesh, 11.4 pct; -35 +I50 mesh, 60.5 pct; -150 mesh, 25.0; total, 100 pct; moisture in bank, 20.0 pct; weight per cu ft in bank, 120 lb. The —150 mesh fraction may increase to as much as 35 pct in adjacent areas. When thoroughly elutriated, the matrix has a relatively slow settling rate, which is an important factor in permitting lower pipeline velocities without choke-ups. Exact data is not available to evaluate settling rates. For a factor of 100 a suspension of clean building sand in water is suggested. When pumping long * Pebble is a commercial designation for the coarser fraction of finished phosphate from a washer, usually +14 mesh. distances, a quick settling matrix allows the coarser solids to settle out along the bottom of the pipeline, causing drag, turbulence, and increased friction. With a slow settling matrix as at Noralyn, turbulence acts to keep the solids in suspension at a lower friction head, regardless of the pumping distance. When the pebble content of the matrix, i.e., the + 14 mesh fraction, is in excess of 10 pct of the total solids, trouble may be expected from settling out even in normal pumping distances. To prevent choke-ups and maintain tonnage, an additional pump must be added in the long runs, where one pump would otherwise be satisfactory. A typical pulp handled is: total volume, 7800 gpm; water, 4500; solids pumped per hr, 4200 lb; sp gr pulp, 1.4; percent solids in pulp, 46.; pipe size, 16-in. ID; pulp velocity, 12.85 fps; probable critical velocity, 10 fps, as below this minimum velocity choke-ups would be numerous. In calculating friction heads the Armco handbook is used where a roughness factor based on 15-year-old pipe is set up. Because the pipe used in pumping matrix is smooth and polished because of the scouring action of the phosphate and its silica content, the head losses in the Armco table for water are practically the same as in pumping the Noralyn matrix through smooth pipe, plus the fact that conditions vary widely over short periods, making accurate determinations difficult to obtain. New pumps and pump changes are being tested continuously and a wealth of data built up. This has resulted in a substantial improvement and lower relative costs in pumping matrix. The Florida phosphate industry is constantly seeking to offset higher wage and material costs with improved technique. Until a few years ago a 12-in. discharge pump was commonly used, with heads as low as 80 ft. Sizes have gradually increased and heads more than doubled. For example, the following pump was placed under test at the Noralyn mine: make, Georgia Iron Works; size, suction 16 in., discharge 14 in.; impeller, 39-in. diam; motor, 600 hp, slip ring; full load speed, 514 rpm. The results were increased head, higher capacity than the older design, with fewer pumps in the line from mine to washer.

Jan 1, 1953

By J. A. Barr, R. B. Burt, I. S. Tillotson

DISCUSSION Howard Howie (Knoxville, Term.)—The authors are to be congratulated on the presentation of a paper containing so much valuable information on the pipeline transportation of phosphate, as there is very little literature on the subject. The writer is especially interested in the paper, as he conceived the arrangement of the Akin and Godwin plants and was in charge of the design work and the engineering incident to their construction. The Akin and other phosphate deposits in the Tennessee phosphate area lie on beds of limestone that are very irregular. The limestone beds, after the phosphate matrix has been removed, are similar in appearance to land severely eroded by the action of water and denuded of top soil. Depressions in the limestone, called cutters, are irregular in depth with vertical or overhanging walls, having the general appearance of cracks in dried clay. They change abruptly in direction, width, and depth, and vary on the Akin tract from 1 to 25 ft in depth and from 1 to 50 ft in width. Pinnacles of limestone commonly occur in the cutters which appear, when exposed, like small clifflike islands in a river. Limestone floats also occur. The phosphate matrix fills the cutters and covers the uncuttered areas, the thickness of the cover varying continually and sometimes rather abruptly. It occurs generally as stratifications of phosphate rock and clay of varying thickness. The phosphate rock in the matrix varies in hardness and in percents of silica, lime, iron oxides, and fluorine, and the clay varies in toughness. In some places the deposit consists of narrow strata of rock almost devoid of clay streaks. In other nearby locations the clay will predominate. When it is excavated, the phosphate rock breaks into thin irregular lumps, locally known as plate rock. Limestone lumps are also excavated with the matrix. Akin plate rock is generally much softer than that occurring in other deposits in the area. Because of the above described physical and chemical variations of the excavated material, the resultant slurry varies in size distribution, specific gravity, and percent of slimes. When the rock is soft or when there is an increase of clay, the slime fraction is greatly increased as it passes through pumps and pipelines, resulting in reduced pipe friction. It is obvious that the longer the pipeline the greater the reduction of coarse fractions into fines, causing a decrease in pipe friction that cannot be accurately evaluated. The matrix is mined with a dragline that drops it into a hopper with a grid composed of 9-in. parallel bar spacings located above the hammer mill. The matrix on, and passing through the grid, is subject to the action of powerful sprays which wash it down to the hammer mill, together with any limestone lumps that are not removed before passing through the grid. The hammer mill reduces the feed to lumps of plate rock and clay, most of which will pass through the 8-in. pump suction. The mixture discharges into a pool containing the pump suction pipe. Water from a hydraulic nozzle moves the mixture to the pump suction intake. The pump, driven by a variable speed motor, is the same size as the pumps mentioned on p. 279. Provision is made to remove any lumps that lodge in a bend in the suction pipe in a manner similar to that used in the Florida phosphate fields. The hammer mill and pump units are mounted on wide steel skids so that they can be moved as the mining operation progresses. The discharge from the pump flows through an abrasion-resistant spiral welded steel pipe 81/4 in. actual inside diam, 8 in. nominal diam, for a maximum distance of 2200 ft, which is the limiting pumping distance for one pump. This pipeline, referred to hereafter as pipeline A, discharges into a ball mill without balls, which in turn discharges into a rotary screen attached to it that separates the slurried matrix into 11/4-in. oversize and undersize fractions. The oversize is returned to the mill for further reduction; the undersize is pumped to a Dorrco washer and then flows into a hydroseparator 160 ft in diam. In spite of the size reduction in the hammer mill and the blunging and washing of the slurry in its passage through the pump, pipeline, mill, and washer, the discharge to the hydroseparator frequently contains mud balls almost perfectly spherical. Sometimes the discharge from the 16,000-ft pipeline at Godwin contains mud balls the size of bird shot and smaller. This pipeline will be referred to subsequently as line B. Liquid caustic is added to the slurry at the Akin plant before its passage through the hydro-separator, which decreases the size of particles in the overflow by dispersion. In passing through pumps 1, 2, and 3 and pipeline B, the slime fraction in the underflow is increased by abrasion and blunging and also by continuing dispersive action of the caustic. The matrix for use in the experimental tests referred to on p. 279 was obtained from three small surface openings on the Akin tract that were made previous to the purchase of the tract by the Authority. Matrix used in the 2 and 4-in. experimental pipeline tests was taken from the three openings and proportioned to obtain a sufficient quantity that would be fairly representative of the average in the Akin deposits. Prospecting samples of matrix had been obtained from drill holes which showed no small variation in physical and chemical properties. Some of the physical variation is evident from the size distribution of solids in samples taken during the tests covering line B flows so thoroughly made by the Authority und'er the direction of Mr. Burt, see Table V, p. 280. Hydraulic gradients for a pipe of 8-in. diam were derived from the 2 and 4-in. pipeline tests using the so-called representative matrix as above described, and plotted on the profile of pipeline B. Gradients of other materials in slurry form passing through pipelines that bore some similiarity to the Akin matrix slurry were also plotted. After a study had been made of the hydraulic gradients plotted on the profile and the varying slurry flow that would probably occur during actual operation, three pumps were ordered, referred to as No. 1, 2, and 3 on p. 279. No. 1 and 2 pumps were installed and the third kept in reserve should the operation of 1 and 2 pumps prove satisfactory, since installation of the third pump would require an attendant, as well as the laying of 5400 ft of pipe to supply it with seal-water from the Akin plant. Subsequently, it was found desirable to install the third pump to maintain capacity when the slime fraction was low and the coarse fractions were large. Reference to Fig. 6 will show that the flow in B line goes upgrade in three locations. At the outlet at Godwin, the slurry flows between two 45" bends for an approximate distance of 18 ft to rise above the ground a sufficient height to discharge into a launder feeding the first classifier. This condition requires extra energy, which is taken care of by keeping the hydraulic gradient a sufficient distance above the high points. Although there are rather heavy upgrades in the line, the choking condition that might occur at the

Jan 1, 1953

By G. M. Schwartz, D. M. Davidson

THE Duluth gabbro outcrops containing sulphides of copper, nickel, and iron are located on both sides of State Highway No. 1 an airline distance of 8.5 miles southeast of Ely in northeastern Minnesota. The region of known sulphide occurrences includes parts of sections 5, T. 61 N., R. 11 W., and parts of sections 25, 26, 32, 33, and 34, T. 62 N., R. 11 W. These sections, given in Fig. 1, are all in Lake County, Minnesota. Part of the area, which lies entirely within the Superior National Forest, is shown on the topographic map of the Ely quadrangle. The original discovery was made in 1948 when a small pit was opened in weathered gabbro rubble for use on a forest access road. A shear zone had caused unusual decomposition in this glaciated area, and the resulting copper stain was noted by Fred S. Childers, Sr., an Ely prospector, who began searching the outcrops along the base of the intrusive. He was joined in further exploration by Roger V. Whiteside of Duluth. In the summer of 1951 a small diamond drill was moved into the area and a hole 188 ft deep was drilled, passing through 11 ft of glacial drift into sulphide-bearing gabbro. This paper is a preliminary report on the geology of the newly discovered ore. The Duluth gabbro is one of the largest known basic intrusives and may be defined as a lopolith.' It extends northeastward from the city of Duluth as a great crescent-shaped mass that intersects the shore of Lake Superior again near Hovland, 130 miles to the northeast, see Fig. 2. The distance around the outside of the crescent is nearly 170 miles. The form of the intrusive is simple at Duluth where it ends abruptly north of the St. Louis River; at the east end, however, the gabbro splits into two elongated, sill-like masses separated mainly by lava flows and characterized by minor irregularities. The outcrop reaches a maximum width in the central part where it is about 30 miles across, and a maximum thickness of about 50,000 ft. It may be significant that the sulphides occur at the base of the thickest part. The lopolith has segregated into rock types ranging from peridotite to granite. The most abundant types are olivine gabbro, gabbro, troctolite, anortho-site, and granite. Of lesser importance quantitatively are peridotite, norite, pyroxenite, magnetite gabbro, and titaniferous magnetite. Grout estimates that two-thirds of the gabbro at Duluth is olivine gabbro. Variations in the percentages of plagio-clase, augite, olivine, and magnetite-ilmenite constitute the only essential differences found among the basic rock types. The predominant mineral is plagioclase, mainly labradorite. Plagioclase and olivine seem to have crystallized early, and the olivine rich rocks, usually troctolite, are found in the lower part. Segregations of titaniferous magnetite are abundant near the base of the gabbro along the eastern part and also occur far above the base. These have recently been described in detail by Grout.' Near the top, segregation has produced a gradation to granite, or "red rock," as it is known locally. This consists of quartz, red feldspar, and hornblende. The red rock forms a zone with a maximum width of nearly 5 miles but is quantitatively unimportant from Duluth northward for 35 miles. In Cook county, where the gabbro splits, each of the two sill-like masses has a red rock top somewhat thicker in proportion to the gabbro below than in the main central mass. The intrusive ranges from coarse to medium in grain size and from granitoid to diabasic in texture. Throughout much of the Duluth gabbro in Minnesota banding and foliation are well developed, as Grout has emphasized.V he bands are mainly a result of variation in the percentage of minerals, as in troctolite with alternating bands high in olivine and in plagioclase. A few bands may consist largely of one mineral, as is true of some segregations of magnetite. Many of the banded rocks show a clearly developed parallelism of platy plagioclase crystals, and both banding and foliation are believed to conform to the floor of the lopolith. Throughout its extent in Minnesota the Duluth gabbro dips east and south toward Lake Superior. It is generally believed to extend beneath Lake Superior and is found as a smaller mass exposed along the north side of the Gogebic district in Wisconsin and Michigan. The dip at and near the base ranges along most of its length from 20 to 40°, but at places the internal banding dips even more steeply. The dip of the upper part is much less, and if it is assumed that the flows along the north shore of Lake Superior are a dependable indication, it does not exceed 15". The formations shown in Table I which are intruded by the gabbro range from Keewatin to Middle Keweenawan in age. They present a significant picture. At the top, the gabbro and its accompanying

Jan 1, 1953

By F. Gordon Smith

ALTHOUGH several geological indicators of the critical type are known, including quartz inversions and decomposition of hydrous minerals such as serpentine, there are very few of the general type. Solid solutions are excepted, but the limitations of use are very restricted and interpretations are sometimes ambiguous. General methods for determining temperature and pressure conditions during the crystallization of minerals would have considerable scientific and economic value. It is not the purpose of this paper to discuss the various methods of geological thermometry and barometry, but to present one general method, applicable to all minerals, and to describe what progress has been made in the methods of measurement. The general method, in brief, is a study of the stress conditions in and around various types of foreign inclusions which are trapped in minerals during growth. The method depends upon the fact that any homogeneous gas, liquid, or solid will in general have coefficients of thermal expansion and volume compressibility different from those of any given mineral. Therefore stress must develop in and around all types of inclusions in minerals if the temperature or the pressure, or both, are changed from the conditions which prevailed during the growth of the mineral. The methods of measurement consist of determinations of the temperature-pressure conditions of fit of the inclusions in the host mineral. The types of inclusions in minerals are: I—gas, or liquid plus vapor, when observed at room temperature, due to crystallization under pneumatolytic conditions; 2—liquid, or liquid plus vapor when observed at room temperature, due to crystallization under hydrothermal conditions; 3—glassy solid, or devitrified glass, due to crystallization under magmatic or high temperature metamorphic conditions, in a siliceous liquid; and 4—crystals, due to overgrowth of other minerals crystallizing simultaneously or of other minerals which crystallized previously. A survey of the literature shows that much valuable earlier work on inclusions, especially that car- ried out in England in the last century, has dropped out of current knowledge. The following is a brief summary of the significant contributions to the problem up to the present day. Davy in 1822 asserted that fluid inclusions in minerals consist of an aqueous solution of salts and a gas bubble, the whole being either at lower or higher pressure than atmospheric.' At intervals from 1823 to 1862, Brewster contributed information concerning other types of inclusion consisting of 1—aqueous solution, a much more expansible liquid, and a gas; 2—aqueous solution, salt crystals, and a gas; and 3—the very expansible liquid and a gas. The very expansible liquid fills the gas space between 20" and 30°C. Compression strain effects were seen around inclusions in diamond, topaz, and other minerals.'-" Sorby in 1858 and 1869 further advanced the study begun by Davy, stating that fluid inclusions represent a sample of the mother liquor of crystallization and that the degree of filling of aqueous inclusions at room temperature defines the temperature-pressure relations during formation of the host. The degree of filling may be measured by determining the minimum temperature of filling of the inclusion by the liquid phase. The very expansible liquid in some fluid inclusions is liquid carbon dioxide. The temperature at which salt crystals in fluid inclusions completely dissolve in the fluid is the minimum temperature of formation. Inclusions of glass or devitrified glass indicate crystallization from a melt. Inclusions of crystals in minerals are often centers of strain, which may be seen by optical effects or by radial tension cracks. Sorby realized that an analysis of stress-strain relations about inclusions could be used to provide precise data on the temperature of crystallization, but the matter was never pursued.' , Hartley (1876, 1877),".'" Hawes (1881)," Wright (1881),'V ohnsen (1920),I3 and Holden (1925)"

Jan 1, 1953

By Peter S. Jack

"IntroductionTHE ORES treated at the concentrator of the Britannia Mining and Smelting Company, Limited, Britannia Beach, B.C., have always contained some lead, but it was not until 1950 that the combination of lead headings and lead price was such that recovery of this metal at Britannia became worthwhile. In that year, with the mining of a new orebody, the lead in the mill feed was raised from 0.07 per cent to 0.15 per cent. Chalcopyrite, sphalerite, and pyrite concentrates are produced by flotation at Britannia, •and 95 per cent of the lead in the mill feed reports with the chalcopyrite concentrate, so that the rise in lead headings was reflected almost wholly in the lead content of the copper concentrate. In 1950, investigation was started to determine if some of this lead could be recovered economically."

Jan 1, 1953

By C. R. Dodson, D. Goodwill, E. H. Mayer

The paper summarizes the historical background of the pressure-volume-temperature analyses of reservoir fluids, the errors involved in both the sampling and testing of reservoir fluids, the type of information required of a PVT determination, and the field conditions that limit the application of any one analysis. Particular emphasis is placed on the necessity for approximating as closely as possible the liberation sequence occurring in the producing formation, flow string, and surface separators. A combined differential and flash or "composite" liberation is suggested as the best means of approximating this liberation sequence. HISTORICAL BACKGROUND Petroleum reservoir engineering commonly is considered to be one of the newest fields of petroleum science, yet much work of a theoretical and intuitive nature was done many years before the modern techniques of reservoir analyses were developed. The period 1910-1924 saw considerable work in the field of reservoir behavior done by the U. S. Bureau of Mines. This work:.' although entirely theoretical, pointed out the importance of gas in the recovery of oil from the reservoir. The statement by J. 0. Lewis that 20 per cent or less of the oil originally in place in a pool was recovered from the ground under uncurtailed production conditions caused some operators to re-examine and modify their production methods. However, though these works showed methods of production that have subsequently resulted in greater oil recoveries, they in general went unnoticed, even though there was a fear that the nation's petroleum resources were being exhausted. The period 1924-1933 saw the industry take considerably more interest in reservoir behavior because of an unfounded fear of its inability to replace oil reserves, the possibility of government regulation, and the energy of one man, Henry L. Doherty. Doherty aroused heated discussions in the industry concerning conservation. To prove or disprove his theories the first experimental work on the reservoir behavior of petroleum was undertaken. The papers of Dow and Calkin,' Beecher and Parkhurst," and Mills and Heitheckere are classics although their experimental procedures were crude. These papers proved that the properties of petroleum in the reservoir are quite dissimilar to the properties measured at the well head. Gas dissolved in the oil phase was recognized as having considerable importance as had been predicted by the earlier theorists. Slightly later Miller and his co-workers assembled the first text correlating all the known data on the reservoir behavior of petroleum and used, these data to show the economic value of conservation. Quantitative application of pressure-volume-temperature analyses of reservoir fluids was given in the paper of Coleman, Wilde, and Moore"; this work showed that with sufficient laboratory and production data prediction of reservoir behavior was possible. The refined sampling and labora-

Jan 1, 1953

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953