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INTRODUCTION Engineering studies of many near surface coal deposits that are amenable to strip mining can be enhanced and expedited by the application of computer techniques for defining coal reserves and overburden and intraburden yardage and their stripping ratios. The case study discussed herein could be from the western coalfields of Colorado, Wyoming, or Montana; the lignite deposits of the Dakotas or Texas, or from the strippable coal seams of the midwest. Because the techniques can be applied so universally, the actual map locations are not identified. The same computing principles apply to one seam or multiseam deposits, and the capability of the computing programs and plotting routines to display the coal seams in plan and sections provide excellent base maps for further engineering planning and mine layout studies. MANAGEMENT OF DRILL HOLE DATA Drilling for coalfield information is usually done at much wider centers than for other mineral deposits. The geologic logs of the holes are generally quite simple, and frequently record only major lithologies and depths to the top and bottom of the coal seams, together with hole collar survey information. A header card is prepared for each drill hole showing: Hole ID Northing Fasting Elevation Azimuth Dip The header card can be followed by any number of downhole lithologic intercept records: [Hole Depth Lithology Hole ID From-To Coal] Less data errors occur if the computer cards are punched directly from drill hole logs, thus eliminating opportunities for mistakes in transcribing data. All arithmetic manipulations should be left to the computer to avoid as much human error as possible. The SURVEY program is run over the raw data file and all lithologic intercepts are computed and defined in XYZ space. BOUNDARY SURFACES-COAL SEAMS AND LITHOLOGIC UNITS The most useful computer program for defining coal seams in 3D space is a linear inter-

Jan 1, 1980

By L. O. Howard

THE practice of using acid-lined converters at the plant of the Old Dominion Copper Mining & Smelting Co. was discontinued early in January, 1913, and they were replaced by basic-lined converters. The new equipment consists of one electrically operated 12-ft. upright converter stand and two basic-lined shells for same. These shells are provided with twenty-four 1 1/4-in. tuyères. The mouths are 5 ft. in diameter. Owing to the fact that there is no bedding system or other large storage capacity between the mine and the smelter, the furnaces must handle as fast as produced ore and concentrates, which may vary considerably from day to day, both in tonnage and copper content. Consequently the converter is often crowded to its utmost capacity by the frequent fluctuations in the daily matte supply. From the foregoing, it will be seen that in no way can the converter be favored by running light charges or by transferring to it from other stands in operation. Neither can it regularly be allowed to cool between blows, and only occasionally can it be run at as low a temperature as might be wished. No copper precipitate or other foreign material high in copper is available to help out the tonnage. Repairs and alterations or the removal of defective tuyères must wait until such time as a slight falling off in the matte supply-allows the converting operations to ease up. These variable conditions all combine to interfere with the systematic operating of the converter.

Jan 7, 1914

By Robert Franke

In view of the prominence which the conical mill has attained in the fine-crushing field within the few years since its introduction, the following comparison with its more mature forerunner, the Chilean mill, based on extensive tests, is submitted in the interest of the milling profession. Soon after designing the concentrating plant of the Miami Copper Co. in 1909, the Hardinge conical mill made its appearance in the milling forum. Its possibility as a suitable crushing device for the plant was well recognized, but in view of the lack of commercial demonstration, at the time, as to capacity, efficiency for desired product, and the still more uncertain factors of cost of maintenance and power consumption, it was deemed that the immediate adoption of this machine throughout the plant would be a hazardous undertaking. For these reasons it was decided to equip the majority of the immediately required units of the plant with Chilean mills, the fine-crushing proficiencies of which were better known, and one section with Hardinge mills, to serve as a test unit for the guidance of future installations and replacements. Thereby, after 1.5 years' operation with both types of mills, a thorough test as to metallurgical efficiency and cost economy has been obtained. The conical mill used in these tests is the 8-ft. Hardinge pebble mill, having a cylinder 22 in. in length. The cylindrical portion of this mill is lined with cast-iron liner plates, and the conical extensions with silex bricks bound together by cement. Each liner plate carries a projecting lifter, the function of which is to increase the height of drop of the lifted material. Danish No. 5 pebbles, obtained from the coast deposits of Denmark, are used for the grinding charge. The Chilean mill used is a fast-running, 3-roller, 6-ft. Saturn mill, with screens of 0.037-in. opening. The feed to these mills is the oversize of Callow screens having 0.029-in. openings, which follow rolls crushing to 0.5 in. For the ore of this mine, a moderately hard but very fissile schist,

Jan 1, 1914

Joseph E. Thropp, Jr., Indiana Harbor, Ind.:—To what do you attribute the fact that in some localities the by-product coke sells at a premium over the ordinary bee-hive coke for foundry use ? If the cell-structure is preferably soft and rather thick in coke for foundry use, as I understand it, do you mean that by-product coke has soft and thick cell-walls ? William H. Blauvelt, Syracuse, N. Y.:—As I say in one of the paragraphs of my paper, the tendency seems to be towards the manufacture of foundry- and furnace-coke under somewhat different conditions. The development of the best cell-structure in coke, of course, has not reached perfection, but we are making progress, and we are inclined to believe that under ordinary conditions the best furnace-coke, that is, coke with the hard cell-wall and the well-developed cell, is produced at fast coking-time and high heats, whereas the best foundry-coke seems to be produced at somewhat lower heats. In one of our plants we are making furnace-coke in 16-hr. coking-time, and foundry-coke in 20-hr. time. Foundry-men want the strong, tough coke. I think the furnace-men present will agree that the best furnace-practice requires a hard coke, with a well-developed cell-structure. Replying to the question as to the reason for higher prices being realized for by-product foundry-coke than for bee-hive coke, of course, the immediate reason is that it suits the foundry-men better. Perhaps one cause may be that we are able, by the selection of coals, which is not usually practicable at bee-hive plants, to get a quality and analysis best suited to foundry-work, with high carbon-content, and with cell-structure and physical strength especially suited to the foundry-men's ideas.

Jan 1, 1913

By Meredith Johnson

THE year 1924 saw little change in the production of oil and gas it either Pennsylvania or New York. In the early months of the year the price of Pennsylvania crude oil, $4.00 to $4.50 a barrel, was sufficiently high to cause operators to lay plans for rather extensive drilling opera-tions. But when, in August, the price dropped to $2.85 a barrel, there was no inducement for new work and drilling was curtailed. In spite of the curtailment, however, the combined production of the two states for the year showed a slight increase over 1923, the production being 8;859,000 bbl. in 1923, and 8,901,000 bbl.1 in 1924. The increased production was due entirely to. the continued development of flooding operations in the Bradford field, all other oilfields showing a decline for the year. TABLE 1. Production of Crude Oil in Pennsylvania and New York for the Last Ten Years a Production, Barrels Production, Barrels Year Year Pennsylvania I New York Pennsylvania I New York 1915 7,838,000 888,000 1920- 7,438,000 906,000 1916 7,593,000 874,000 1921 7,418,000 988,000 1917 7,733,000 880,000 1922 7,425,000 1;000,000 1918 7,408,000 809,000 1923 7,609,000 1,250,000 1919 8,137,000 851,000 1924 7,535,0006 1;366,0006 a U. S. Geological Survey figures. b Estimated. Much of the drilling in the southwestern part of Pennsylvania was done in search of gas. Natural gas in Pennsylvania is fast being recognized at its true worth and the increased prices allowed 'the gas companies for their product induced quite a bit of new work. The relative importance of natural gas compared with manufactured gas is shown in Table 2.2

Jan 3, 1925

By Ronald K. Linde

Metastable Ag-Cu solid solutions at two compositions beyond the maximum limits of solubility obtainable by quenching from the solid state were obtained by rapid quenching from the liquid state. The process of transformation of the metastable solid solutions into the equilibrium phases was studied by means of X-ray diffraction intensity measurements and electrical-resistance measurements; metallographic examination was also performed. Results are compared with those for an alloy quenched from the solid state at a composition which exists as a solid solution at elevated temperatures. Activation energies for the trans-formation were computed to be 33,600 * 2500 and 33,100 * 2000 cal per g mole for the 60.1 and 75.0 at. pct Ag;Cu compositions, respectively THE kinetics of precipitation in supersaturated solid solutions obtained by quenching from high temperature has been thoroughly studied in many alloys, and detailed investigations of the early stages of nucleation and subsequent growth of the equilibrium phases have been carried out. All of these studies have been made on alloys quenched from the solid state, however, and it is the purpose of this paper to present some of the results on the kinetics of transformation of metastable solid solutions in Ag-Cu binary alloys whose compositions lie outside of the solid-state limits of solubility. Limits of solubility in the solid state can be increased by rapid quenching from the liquid state. This was first demonstrated by Falkenhagen and Hofmann, who obtained appreciable increases in solubility limits of the elements of the first transition series in aluminum by rapid cooling of liquid alloys through contact with a copper mold maintained at liquid nitrogen temperature.' The same basic idea of cooling a liquid alloy by conduction onto a substrate rather than by convection of a gas or liquid (conventional quenching) has been recently revived and extended to very high rates of cooling by Duwez and his collaborators. The new technique was first applied to Ag-Cu alloys because the existence of a eutectic in this system is not predicted by the Hume-Rothery rules of alloy phase formation. Rapid quenching from the liquid state resulted in metastable solid solutions at all concentrations. The kinetics of decomposition of these metastable solid solutions containing 60.1 at. pct Ag;Cu (eutectic composition) and 75.0 at. pct Ag;Cu is the subject of the present paper. EXPERIMENTAL TECHNIQUES Alloys were made in 10- to 20-g heats using silver of purity 99.99 pet and copper of purity >99.999 pct. Components were weighed accurately to 0.1 mg and melted by induction heating in an alumina crucible under an atmosphere of hydrogen. Weight losses amounted to less than 0.02 ~ct in all cases. Rapid cooling from the liquid state was achieved in an apparatus of the type described by Pietrokowsky. 3 In this technique a freely falling drop of molten alloy is caught between a stationary anvil and a fast moving piston, both anvil and piston being lined with copper. The resulting foils were approximately circular (about 2 cm in diam) and from about 50 to 150 u in thickness, depending on the pressure driving the piston. Metallographic samples were prepared for polishing by edge-mounting foils in Quickmount. The mostef-fective etching procedure was found to be: 10 parts NH4OH (concentrated), 1 part H2O2 (30 pct), 5 parts H2O, swab for 5 to 10 sec. The transformation of the metastable alloys to equilibrium was followed by X-ray diffraction and electrical-resistivity measurements. The peak intensity and the integrated intensity of suitable Bragg reflections of the metastable and stable solid solutions were studied with a Norelco dif-fractometer, using nickel-filtered copper KO radiation. The peaks were step-scanned at intervals of 0.05 deg. Using either a Kelvin bridge or a null circuit with a Leeds and Northrup K-2 potentiometer, the changes in electrical resistance due to phase transformation were measured for specimens cut into strips about 20 mm long and 4 mm wide. All resistivity measurements were carried out at liquid-nitrogen temperature. The isothermal heat treatment was accomplished by sealing the samples in argon-filled aluminum containers with stainless-steel O-rings. Containers were then suspended in wax baths with temperatures in the

Jan 1, 1967

By R. C. Patterson

In view of the circumstance that very few important changes have been made within the last 15 or 20 years in the equipment of rod and wire mills, the description of a new process introduced by Grenville Mellen, of LleweIIyn Park, N. J., to take the place of the present laborious system of producing rods of lead, zinc, brass, copper, aluminum, etc., may be interesting to members of the Institute. This new process consists in the production of cast rods at one operation in a small continuous casting machine. The hot liquid metal is transferred from the melting crucibles directly into an endless chain of mold blocks in the machine, where solidification takes place, and the rod comes out continuously in a solid form at one end as long as the molten metal is supplied. The operation of these mold blocks so as to produce a solid rod of uniform structure constitutes an important part of Mr. Mellen's invention. The machine (Figs. 1 and 2), 12 ft. in height over all, 2 by 3 ft. in horizontal cross-sectional area, and 6,000 Ib. in weight, has a framework of cast iron, holding in position two endless chains of mold blocks, which are made in sections and join in center alignment. The mold orifice is made up of these mold sections, into which the liquid metal flows. The molding chains are composed of steel blocks, grooved on one face to form the molding cavity, and linked together with flexible joints. Each block is carried on four rollers which guide the chain around the end sprockets and carry it in its course through the machine. The accuracy of alignment requisite to the production of a perfect rod in the mold groove formed by these sections is secured by careful machine work, and by building the four ways, down which the alignment takes place, so that two of the sides are fixed permanently, whiIe the opposite sides are held to their position by spring pressure. The guides carrying the molds, while in casting position, are water-cooled square tubes. The length of this machine is somewhat indeterminate. A certain amount of both time and cooling surface is required to solidify the metal jn the mold; and one may either use a long molding chain and run it fast, or a shorter chain and run it correspondingly slower. We have found,

Jan 1, 1916

By George Smith

IN discussing present-day business and industrial troubles we easily drop into the habit of clinical diagnosis. Talk of this kind, with its emphasis on suspicious symptoms and abnormal tendencies, makes us all morbid. As an English essayist has put it, we may thus induce a melancholy, temper that simply in-vites the ministrations of social and political quacks. It is far better-because nearer the truth-for us to recognize that our condition is in no sense diseased, that our body politic, social and economic, is suffering merely from growing pains; that America is not de-cadent-indeed, that any lapses from staid normality are traceable to the, excesses of youth. Our chief .trouble, then, is only that our industrial state is still young; it may be that we have been growing too fast. The growth in the industrial development of our country from pioneer days to the present time has been marvelous. Too many of us, however, take all this as a matter of course-we credit this record of American progress to our American genius alone. Too often we overlook the fundamental relationship between resources and progress-that man is aided and even guided by Nature. The fact is, social advance, indus-trial progress, national prosperity all have their ma-terial basis in natural resources. In furnishing the needed mineral raw materials to the great manufac-turing industries of the United States there has been no halt, but rather a general acceleration. No other phase of American activity can show-equal advance. As the decades have passed, the winning of mineral wealth has progressed from the role of a stimulus for western exploration to that of the foundation for nation-wide business. In 1890 the Sherman law was passed; since then the population of the United States has about doubled. Since then, too, thevalue of the annual product of the mines of this country has increased better than eight-fold-from 650 millions to 51/ billions of dollars. Since then the four largest branches of the mineral industry, which supply the iron and copper, the bituminous coal and petroleum-the bone and sinew and the energy of all other American industries-have increased their annual output nearly ten-fold as to value and six-fold as to quantity. Such a growth in the volume of mineral output must be taken as a true measure of the ex-ceptional service rendered by the mines of the United States. Not only is this a much larger country than it was 38 years ago, but its growing mineral industry has met demands that have been out of all proportion to the growth of the population.

Jan 8, 1928

By David C. Russell

The Department of the Interior used to be a quiet, noncontroversial, almost boring agency. It, after all is the fifth oldest of the Departments, and as an old line Federal agency it has studiously performed its preservation and resource management functions in a caretaker mode--though some would say more "undertaker" than "caretaker"--locking up the body and soul of America piece-by-piece. Yes, quiet, serene. That is until Jim Watt showed up. And we have all seen that version of Mt. Vesuvius which resulted--only it was the environmentalists who blew their tops. Ronald Reagan chose Jim Watt as Secretary of this fine old agency to prove that one-third of our Nation's land and over a billion acres on the Outer Continental Shelf can work for this Nation. At the foundation of President Reagan's charge to Secretary Watt is a belief in the tenets of the free enterprise system, and in the individual freedoms upon which this country was founded. There are those who don't share this belief in democracy and free enterprise, and those who believe this 205 year experiment called the United States of America will fail. Nikita Krushchev said "we will bury you"--obviously he didn't agree with our system. An Italian sociologist, Franco Ferrorotti, said bureaucratic stagnation will kill capitalism. Certainly we have all felt the ravages of bloated bureaucracies. Perhaps one indicator in the United States is the Federal Register, that daily compilation of Government's largesse. In 1970, 20,000 pages of the Federal Register were published. A decade later, in 1980, that volume had quadrupled to 80,000 pages. The Federal bureaucracy can stagnate from excessive budgets as well. The Interior Department spent $60 million on administering Federal coal leasing in 1981. That's nearly two bits a ton for every ton of coal leased in 1981. You wouldn't stay in business very long if your administrative overhead on inventory was that outrageous. But the pessimism of our critics is apparent from more than red tape and bloated budgets. For decades America has been fasting--consuming too little of America's wealth of minerals, subsisting instead on a diet heavily reliant upon mid-east oil, with little emphasis or concern for inventorying and developing domestic energy and mineral resources. Economics--yes. But short-term, short-sighted economics. Excessively dependent upon foreign imports, of oil, cobalt, chrome and other strategic minerals, the U.S. measures its time before another embargo--or fallen Shah, or Soviet manipulation, or Saudi shift, or, as we witnessed in Egypt, assassination--an untimely loss to mankind and efforts to bring peace to the troubled mid-east. These disruptions, in addition to their tragic human tolls, impair the free world's security. Huge chunks of the United States have been locked away in dozens of single land use categories in the name of conservation, with only the foggiest idea of what resources might be denied the American people-and this at a time of unacceptable levels of energy and strategic mineral imports. More than half and perhaps two-thirds of all Government-owned lands are totally withdrawn from or severely restricted to development under the mining and leasing laws. We must continue to rid Government of the overly zealous restraints which have been keeping us from drawing upon that which can help restore our economy and national security. When we assumed responsibility, the United States was dependent on foreign sources for about 40 percent of its oil. In 1981, our oil import bill was approximately $83 billion--nearly 17 times what it was in 1972. Our reliance on foreign sources for essential minerals is even more disturbing. We must look to other countries--some unfriendly, some unstable--for 22 of 36 strategically critical minerals. Yet the energy resources on federal lands which are owned by the American people could meet our needs for centuries if properly managed. Eighty-five percent of the crude oil yet to be discovered in America is likely to come from public lands, as will 40 percent of the natural gas, 35 percent of the coal, 80 percent of the oil shale, nearly all of the tar sands, and substantial portions of uranium and geothermal energy. Our vast hardrock-mineral wealth includes untapped deposits of essential elements we now import, such as chromium, copper, platinum, and cobalt. The obvious question is, if these abundant resources can help to revitalize our economic strength and to preserve our national security, why aren't we using them to better advantage? To a large extent, the answer can be found in past decisions to restrict public access to the federal estate, thus deferring to us or our successors the tough decisions that flow from Congress' mandate to provide for environmentally responsible development of America's energy and mineral treasures. Here is the legacy this Administration inherited: In January 1981, 7 years after the onset of the Mideast oil embargo: ---Less than 15 percent of federal onshore lands were under lease for oil and gas development; ---No oil and gas leases had been issued in Alaska for 15 years;

Jan 1, 1982

By J. Chipman, J. C. Fulton

Reduction of Si from slag to carbon-saturated iron is a very slow reaction. The rate is nearly independent of stirring but is accelerated markedly by increased temperature. In a slag containing 45 pct SiO2, 38 pct CaO, 17 pct Al2O3, the energy of activation is approximately 130 kcal. AT temperatures of 1450" to 1600°C occurring in the hearth of the iron blast furnace, chemical reactions are normally expected to proceed with great rapidity. Many of the reactions of iron making are indeed quite rapid and attain a condition corresponding roughly to a state of equilibrium before metal and slag are tapped from the furnace. The one conspicuous exception is the reaction by which carbon in the coke or metal reacts with silica in the slag to deliver silicon to the metal. From the practical viewpoint the slowness of this reaction is indeed fortunate, for if it were fast enough to reach equilibrium during the time of contact, it would be difficult to produce pig iron of the desired low silicon content. The one other reaction which under certain circumstances can also be very slow is the transfer of sulfur from blast-furnace metal to slag. In their laboratory exeriments on this reaction, Hatch and Chipman found that at least 5 hr were required for the attainment of equilibrium in a small crucible and that the reaction was not accelerated by increasing the rate of stirring. Subsequently it was shown2 that the presence of a reducible oxide MnO greatly inhibited sulfur removal, and finally that SiO2 itself3 under some conditions has sufficient oxidizing Dower to interfere with sulfur transfer. The kinetics of sulfur removal are now rather well understood,4 and it has been shown3,5 that when the silicon content of the metal is high enough to prevent reduction of SiO,, the desulfurizing process is rapid. Thus the observations of slow removal of sulfur are associated with the coincident slow reduction of SiO2, a process which transfers both silicon and oxygen to the metal phase. It is, of course, the oxygen which interferes with sulfur removal. An explanation of the slowness of the silica reduction reaction has not been obtained. The sulfur transfer process has been shown by the authors5 to be at least partially transport-controlled in the absence of interference by silica. Under the experimental conditions. 99 pct of the total transfer at 1600" was accomplished within an hour. Under similar conditions the reduction of silica may not proceed half-way to equilibrium6 in 8 hr. It is scarcely imaginable that silica reduction could be transport-controlled when the slag contains 44 pct SiO2 and the metal about 1.4 pct C. The experiments reported here show definitely that it is controlled by a slow step or steps in the chemical reaction. One might expect to find such a slow step in the breaking of SiO bonds or in the slow removal of oxygen by carbon at the slag-metal or metal-crucible interface or by bubble formation. EXPERIMENTAL PROCEDURE The experimental procedure used in this investigation was similar to that used in the study of the kinetics of desulfurization.5 A sketch of the graphite crucible and stirrer used in the current work is shown in Fig. 1. The quantity of metal and slag used was adjusted so that the slag-metal interface was located between the top and bottom blades on the stirrer; the top of the slag layer was above the top blade. The stirrer shaft was hollow down to the metal level and served as thermocouple well or optical pyrometer target. Stirring speeds of 0 to 500 rpm were used. A carbon monoxide atmosphere was maintained in the furnace by flushing the gas over the slag surface, except in run No. 220 when it was bubbled

Jan 1, 1960

By G. M. Schwartz, J. N. Gundersen

Utilization of magnetite-bearing taconite from the great Mesabi range of Minnesota is fast becoming a major industry in the state. The planning and early development stages of taconite processing projects have been de-scribed1-3 and an excellent discussion has appeared recently4 concerning the current mining, crushing, concentrating, and pelletizing techniques of the Reserve Mining Co., whose operations lie entirely within the Eastern Mesabi district. The present paper will deal only with some of the geological aspects of taconite utilization in the district, with emphasis placed upon some of the common mineralogical and textural features of the tacon-ites currently being mined or stripped and how these factors generally affect the potential recovery of the iron from the metamorphosed Biwabik iron-formation. The generalized geologic setting of the Eastern Mesabi district is presented in Fig. 1. The small circles on the geologic map, adapted from Grout and Broderick,3 mark the location of drill holes that were available for inspection during this study through the courtesy of Reserve Mining and Erie Mining Cos. The cores from these holes were divided into stratigraphic units and examined for their mineral content. Typical mineral associations and grain fabrics were also determined from hundreds of thin and polished sections. Available metallurgical tests made it possible to determine the probable response of a given variety of taconite to magnetic concentration. The longitudinal section of Fig. 1, projected along the strike of the iron formation, presents the simple stratigraphy of the area. It also shows the uniformly thick nature of the iron formation members in the district as well as a somewhat abrupt thickening of the formation to the west of the probable fault. The stratigraphy of these precambrian rocks has been described5-' elsewhere and need only be briefly reviewed. Historically, the oldest rocks unit, the Giants Range granite (Algoman) was covered by the Animikie group of sediments (Middle Huronian?), consisting of the Pokegama, Biwabik, and Virginia formations. Outcrops of the Pokegama quartzite are locally distributed along the northern limit of the Biwabik iron formation, but they are too limited to depict on the geologic map of Fig. 1. The effects of the intrusion of several small diabase sills within the Virginia and Biwabik formations are obscure because all of these rocks have been subsequently highly metamorphosed, mainly by the Duluth gabbro. The emplacement of the transgressing Duluth gabbro (Middle Keweenawan) and that of numerous peg-matitic veins in the iron formation8 has resulted in extensive contact and metasomatic metamorphism which has locally reconstituted the previously existing minerals of the Biwabik formation, in large part quartz and magnetite, into a wide variety of silicate mineral assemblages9 that have a profound effect upon the re coverability of the remaining magnetite. The entire region has subsequently been eroded and largely buried beneath Pleistocene glacial deposits. Structurally, the strike of the gently dipping Animikie group generally parallels the elongate outcrop pattern of the Biwabik iron formation on the map of Fig. 1. The Animikie group most commonly dips from 5" to 15" to the south-southeast. In this area, the Duluth gabbro pluton is somewhat sill-like, dipping about 30" to the southeast. Projecting these present structures upward, it seems probable that the gabbro once extended over the underlying Animikie group in the Eastern Mesabi district. SELECTION AND PRESENTATION OF DATA Because of the locally intense metamorphic activity in the district, mineralogical variations within the magnetite-bearing taconites are commonly abrupt, both vertically and laterally. Consequently it is difficult to select a single hole or small group of holes whose cores will be entirely representative of all of the district. Two holes have been selected, however, that in a general way represent mineralogical and textural variations that are likely to be encountered in both the eastern and western parts of the district. These recently drilled holes were chosen for discussion because it was possible to log the core and then to place the sample intervals at stratigraphic boundaries prior to preparation of the core for magnetic tube tests.

Jan 1, 1961

By H. C. Fiedler

Heats of high purity iron containing 3.1 pct Si and be -tween 0.0003 and 0.0295 pct N were prepared by vacuum melting ad then pouring while in a nitrogen atmosphere with the pressure between 0 and 90 psi. Strip from a heat with 0.0184 pct N underwent complete secondary recrystallization during the final anneal. Heats with less nitrogen had too few Si3N4 particles to restrain normal grain growth, and the heat with higher nitrogen had too many particles to allow complete secondary recrystallization. In the hot-rolled structure, Si3N4 precipitates only at the grain boundaries, with the consequence that annealing after hot-rolling diminishes the ability to subsequently undergo secondary recrystallization. In contrast to this behavior, ALNprecipitates uniformly in the hot-rolled structure. Under 1 atm of nitrogen, Si3N, in 3.1 pct Si-Fe dissociates between 900" and 950°C; the solubility of nitrogen increases from 0.0010 pct at 900" to 0.0030 pct at 1200°C. The solubility of nitrogen in Si-Fe has been the subject of many investigations. Corney and Turkdogan1 heated a 2.83 pct Si alloy in nitrogen and found the solubility, under 1 atrn of nitrogen, to be 0.0019 pct at 900°C. They claimed that Si3N4 did not form in the alloy above 705°C in 1 atrn of nitrogen. Fryxell et al.2 heated samples of 3.25 pct Si-Fe containing 0.0025 pct N over a range of temperatures and then analyzed for total nitrogen by vacuum fusion and for nitrogen in solution by a modified Kjeldahl technique. At 900°C, they reported the solubility of nitrogen in equilibrium with Si3N4 to be 0.0011 pct. pearce9 found the solubility of nitrogen at 900°C under 0.95 atrn of nitrogen to be 0.0017 pct in a 3.06 pct Si alloy. He reported that Si3N4 does not form above 770°C in 1 atrn of nitrogen. Although internal friction measurements have given somewhat higher values for the solubility,4-6 if the solubility of nitrogen is as low as has been reported by most investigators, and if Si3N4 is stable up to at least 945°C at 1 atrn pressure of nitrogen as reported by Seybolt,7 a small amount of nitrogen in properly processed Si-Fe should be effective in promoting secondary recrystallization. The requirement is that in the final heat treatment there be enough small, well-dispersed particles of Si3N4 to restrain normal grain growth. Fast8 has obtained secondary recrystallization by nitriding high-purity 3 pct Si-Fe after hot-rolling to a thickness of 0.118 in., followed by processing to 0.012 in., and annealing. A large amount of nitrogen, 0.076 pct. was introduced during the nitriding heat treatment, but he has since reported9 that "a few hundredths of a percent" is sufficient. Small amounts of aluminum10 or vanadium" nitride are capable of promoting secondary recrystallization. Heats containing as little as 0.010 pct A1 or 0.042 pct V and from 0.006 to 0.009 pct N underwent complete secondary recrystallization at final gage, whereas heats with lesser amounts of aluminum or vanadium did not.l2 To be reported is the behavior of nitrogen in high-purity 3.1 pct Si-Fe, and the relation of this behavior to the ability to undergo secondary recrystallization. PROCEDURE Ingots weighing 1 lb were made by vacuum melting high-purity electrolytic iron (A104, Glidden Co.) and high-purity silicon (Monsanto Co.). The latter was used in preference to ferrosilicon to insure a low aluminum content. The design of the melting furnace permitted pouring with the furnace atmosphere either below or above atmospheric pressure. Accordingly, at the completion of melting, nitrogen was admitted to the desired pressure and the heat then immediately poured. The ingots were sound, with no indication of porosity. In Table I are listed the heats investigated, the nitrogen pressure at pour, and the nitrogen and oxygen contents as determined by vacuum fusion with a platinum bath at 1850°C, a procedure which insures measurement of the total nitrogen.13 In addition, all heats contained 3.1 pct Si and not more than 0.002 pct C, 0.003 pct S or 0.005 pct Al. It was subsequently found that the quantity of nitrogen contained in the heats in Table I does not necessarily represent that obtained under equilibrium conditions. For example, the ingot poured immediately after 1 atrn of nitrogen was admitted to the chamber contained 0.0093 pct N, whereas an ingot poured 3 min after the nitrogen was admitted contained 0.021 pct N and another poured after a 6-min delay contained 0.029 pct N. While some bleeding of the hot top occurred in the latter instance, the ingot when examined in cross section appeared sound. The ingots were heated to 1325°C in hydrogen and rapidly rolled to 0.080 in. in 3 passes. The roll speed of the final pass was reduced so as to increase the quenching effect of the rolls. The hot-rolled pieces were processed both as-hot-rolled and after heating for 3 min at 900°C in hydrogen. After cold-rolling to 0.026 in., the strips were heated for 2 min at 900°C in hydrogen, then cold-rolled to the final gage of 0.012 in. The loss of nitrogen in going from the ingot to cold-rolled strip was no more than 10 pct. The final heat treatment, which was for the purpose of develop-

Jan 1, 1970

By Saluja, Sunder S.

Man had to learn to break rocks as early as the Stone Age, when they formed his main source of raw material. He started with chipping and over the years has reached a stage where he can employ atomic blasts and break, with one blast, millions of tons of rock. In between these two extremes there have been several stages of development including fire setting, use of the expansion of water on freezing in chipped cracks in cold climates, the use of low or deflagrating explosive black powder in about the 17th century, the use of high explosives with the discovery of nitroglycerine in 1846 by Sobrero, followed by the monumental discoveries of the great Swedish scientist Alfred Nobel in the latter half of the nineteenth century.

Jan 1, 1968

By Harry A. Wahl

Precent fracture design procedures are bared on the total fracture area created. A method to distinguish beI,,.ecn total area and [he propped or effective fracture area has not been available. This paper presents a solution to this problem, applicable to horizontal fractures. The difierences between effective fracture area and torn] area are demonstrared in example calculations. This work is hayed on experimentally determined transport efficiencier of solids in sand-liquid slurries. Newtonian and non-Ne~vtoninn systems are considered. INTRODUCTION Fifteen years after commercial introduction, hydraulic fracturing remains the most successful stimulation technique in the oil field. This success is primarily due to ability of induced fractures to penetrate and alter permeabilities deep within formations. Many fields producing today could not have been developed without the hydraulic fracturing process. Because of wide usage, fracture-treatment design has received a great deal of engineering and research effort. This work, resulting in improved equipment and materials, has increased the benefits from fracture treatments as well as the applicability of the process. A major contribution was the development of fluid-loss additives. Necessarily, the number of parameters to be considered in treatment design has steadily increased, resulting in more complicated design techniques. Almost all present design procedures are based on the precepts set forth by Howard and Fast. Relating the fluid volume lost into the formation, the volume required in extending the fracture, and the total slurry volume injected, they developed an expression for the total fracture area created in terms of pertinent treatment parameters. Fluid loss during treatment was expressed as a function of time for three flow mechanisms. Although modifications of fluid loss equations have been made, the total fracture area concept has remained unaltered. A vast amount of field data indicate that induced fractures must be propped and held open to be effective. A notable exception is the Mesa Verde formation in the San Juan basin. However, analysis of these treatments shows that improved well productivities are obtained when propping agents are incorporated in the treating fluid. Although propped fracture area has been recognized as an important design parameter, a method to distinguish between total area and effective fracture area has not been available. The necessary information on slurry-sand transport in fractures has been lacking. Interest in the propped region of induced fractures is not restricted to areal extent alone. The distribution of sand within fractures is important from the standpoint of fracture flow capacities. Flow capacity affects the increase in well productivity after stimulation. The work of Huitt and Darin4 hows that partial monolayers of sand have large flow capacities compared to thick* dense sand packs. It has been postulated that gelled fluids have the ability to transport sand within the fractures at the deired low concentrations. An early contribution in the area of sand placement in fractures was made by Kern et al.' They studied sand movement in a transparent vertical fracture model. It was observed that the sand tended to settle out in the bottom of the model before moving very far. When the fluid velocity exceeded a certain critical value, all of the sand injected began moving through the crack even though it settled to the bottom. This critical velocity was determined under several flow conditions. Some work on sand movement in horizontal fractures has been reported in Russian publications. Sand movement was studied by Izyumova and Shan'gin' using a transparent "pie-shaped" flow model to simulate a horizontal radial flow system. However, the data were limited, especially in a quantitative sense. Dorozhkin, Zheltov and Zheltow studied the behavior of sand-liquid slurries in a horizontal linear flow model. The quantitative data were restricted primarily to the thickness of sand deposits formed at the bottom of the fracture. An earlier paper provided basic data on the flow of sand in horizontal fractures. This study was designed to yield specific quantitative information on rate of advance of sand particles and pressure behavior under various flow conditions. A comprehensive photographic study was undertaken in a 10-ft windowed flow cell to provide the necessary qualitative and quantitative data. Since the number of potential variables far exceeded the capacity of the initial study, emphasis was placed on the effects of sand concentration, oil viscosity and oil flow rate. A detailed description of these experiments and the results are described in Ref. 9. However. the implications of this work on the fracture design calculations were not discussed. An analysis of these data as well as new data is provided in the following sections. EXPERIMENTAL RESULTS The primary objective of the experimental investigation was to provide information on the rate of advance of the solids in sand-liquid sturries. A 10%-ft long transparent

Jan 1, 1966

By Harry V. Welch

This paper presents a brief discussion of numerous devices and processes which have been utilized for the recovery of values from gases in copper reduction works and describes in greater detail the development and application in recent years of electrical precipitation, more familiarly known as the Cottrell process, to the problems of dust losses with furnace gases in copper-smelting and refining plants. The field for collection of suspended particles in gases is widely extended in our modern complex, congested .and industrialized mode of living, and its satisfactory solution is required by our increasing appreciation of the extravagant waste, unhealthful effects and nuisance which such uncontrolled emission of solid suspensions represents. Much of the special dust-recovery equipment in use today has been developed in one industry and carried over to many others. The early work of Cottrell was with sulfuric acid mists, aimed at the purification problem in contact acid manufacture, but the present uses of Cottrell equipment cover a diversified field—carbon black, combustible gas, oil mists, iron blastfurnace fumes and dusts, cement-kiln gases, as well as the purification of gases in contact and chamber acid plants and its wide and extended use in the nonferrous metallurgical field of copper, zinc and lead, and their associated metals. Dust and fume collection from furnace gases became a problem only with the modern development of large and amply powered auxiliary furnace equipment, which in turn permitted large furnace units, fast driving and large outputs of finished product per unit of furnace capacity. The ancient metallurgist with his small clay pot and hand-operated bellows had too little gas velocity to cause a real dust loss. As furnaces grew in size, flues and stacks were added, and undoubtedly the first observable dust losses were indicated by the deposits in the flue and stack base. Large flues, it was noted, collected more than smaller ones, and the expansion of a portion of the flue into a chamber represented the first serious attempt at recovery of furnace dust losses. For a century or more the settling chamber represented the best of skilled metallurgical practice in recovery of furnace dust, and it may be said to have reached

Jan 1, 1934

By J. Chipman, N. J. Grant, B. M. Shields

The vacuum tin-fusion method of analysis for hydrogen, developed by Carney, Chipman, and Grant, has been modified to permit the analysis of the evolved gases for hydrogen by means of a thermal conductivity cell. A properly prepared sample can be analyzed in 10 min with a probable error of ±0.12 ppm. A study of various methods for storage of hydrogen samples shows that samples can be safely held in a dry ice-acetone bath as long as six days. Storage in liquid nitrogen is necessary for samples to be held one week or more. HE vacuum tin-fusion method, as developed by I- Carney, Chipman and Grant,' is the only analytical procedure which has shown promise of being fast enough for use in the control of hydrogen during steelmaking. It was felt that further simplification and faster speed of operation could be effected by the use of thermal conductivity measurements for analysis of the gases evolved in the tin-fusion method. The application of conductivity measurements to the tin-fusion method is possible because: 1—the evolved gas is essentially a mixture of hydrogen, nitrogen and carbon monoxide with a hydrogen content usually over 50 pct, 2—the evolved gas is collected at a relatively low pressure, and 3— the thermal conductivities of CO and N2 are practically identical while that of hydrogen is very much greater. The major part of this research program was devoted to the construction and calibration of a vacuum tin-fusion apparatus which analyzes the evolved gases for hydrogen by means of a thermal conductivity cell. The second phase of the problem was associated with the development of a procedure for storage of samples prior to analysis. With the rapid quenching method for hydrogen sampling,' which seems to be the most practical for steel mill use, it is necessary that the samples be stored safely during the interval between sampling and analysis if the hydrogen content of the molten metal is to be maintained in the supersaturated solid samples. The thermal conductivity bridge has been used for a number of years in the analysis of certain gas mixtures. An elementary discussion of the theory and practice of gas analysis by thermal conductivity measurements is given by Minter.3 A more comprehensive discussion of the theory and of the various measuring circuits is presented by Daynes.' A complete knowledge of the theory and properties of the thermal conductivity of gases and gaseous mixtures can be gained by a study of the standard textbooks on the kinetic theory of gases."' The existing data on the thermal conductivity of single gases are reviewed by Hawkins: that for a number of binary gas mixtures by Daynes' and Lindsay." The thermal conductivity method may be applied to the determination of the composition of a binary mixture if: 1—the thermal conductivity of the mixture varies monotonically with composition, and 2— the two gases have measurably different thermal conductivities. The greater the difference between the two gases, the greater the sensitivity of the method.10 he method is applicable to the analysis of multicomponent mixtures when all of the gases in the mixture except one have nearly the same thermal conductivity. Fortunately, the mixture of hydrogen, nitrogen, and carbon monoxide evolved by the tin-fusion analysis' falls in this latter classification. The thermal conductivities of nitrogen and carbon monoxide are practically equal; and the thermal conductivity of hydrogen is approximately seven times that of the other two. Therefore, the thermal conductivity of a gaseous mixture of hydrogen, nitrogen, and carbon monoxide at known temperature and pressure can be related directly to the percentage of hydrogen in the mixture by suitable calibration. Usually the thermal conductivity of a mixture of gases is measured at atmospheric pressure where the thermal conductivity is independent of pressure over a wide pressure range. At very low pressures (below 1 mm Hg), the thermal conductivity of gases varies with the pressure. This phenomenon has been utilized in the Pirani vacuum gage for the measurement of pressures in the range of 10" to 10-0 mm of mercury.= Very little has been published concerning the variation of thermal conductivity with pressure at intermediate pressures between 1 mm Hg and 1 atm. However, preliminary measurements indicated that the thermal conductivities did vary with pressure over the range of pressures (up to 10 mm Hg) at which gases are delivered from the vacuum pump. Therefore, the calibration of the thermal conductivity cell had to be planned to include the effects of both gas composition and pressure. Such a calibration chart is shown in Fig. 4. Most industrial applications of the thermal conductivity method of gas analysis have used a compensated Wheatstone bridge circuit containing two

Jan 1, 1954

By R. N. Orava

TO the author's knowledge, only one satisfactory high-resolution technique for etch-pitting dislocations in Cu-Zn alloys has been published.' In that account, pits in 70/30 brass single crystals were produced by etching electrolytic ally in a 30 pct orthophosphoric acid bath. Thereafter, observations were made from surface replicas by electron microscopy. The method of pitting and observation permitted the high resolution necessary for the distinction of individual dislocations in arrays of pile-ups. However, no comment was offered concerning the possibility of obtaining pits which are amenable to optical resolution. Moreover, for adequate results, the electrolytic pitting process is invariably preceded by a polishing stage which could obscure the surface features of interest. Consequently, it would be desirable to be able to delineate, by solely chemical means, dislocations which could be detected by both optical and electron metallo-graphic techniques. This was achieved by the simple expedient of modifying two etchants reported by young2 to reveal dislocations on the (100) planes of pure copper. Single crystals of 70/30 a brass, described previously,3 were sectioned to provide a surface parallel to a set of {100) planes, mechanically polished, and subsequently electropolished at 2.4 v in a solution comprised of 2 parts H3PO4, 4 parts ethanol, and 3 parts water. The inclusion of ethanol tended to inhibit nonuniform surface attack. Etch-pitting was effected by a 2 to 3 sec immersion in a 70 pct aqueous solution of HNO3. The samples were then washed in a fast-flowing stream of water, and rinsed further in distilled water, and ethanol, before drying. It is important to note that this reagent should be either used immediately after mixing, or, if allowed to cool, reheated to about 35°C prior to use. No pitting was obtained at room temperature. Typical results are shown in Fig. 1 where (a) is an optical view of the pitted surface and (b) is an electron micrograph of a silicon monoxide replica shadowed with tungsten oxide. The former is characteristic of a somewhat longer etching time (-6 to 8 sec) which varied with bath temperature. Similar pits accrued from a 1/10 aqueous dilution of another of Young's solutions2—2 M FeC1,6H20 and 7.8 M HBr.

Jan 1, 1968

Large equipment for quarrying and for the various stages of crushing and grinding are the trend for new and existing operations. Included are large size haulage units, fast drilling equipment, impact crushers and large mills capable of high tonnage rates for metallic and nonmetallic minerals. In grinding, large-size mills continue as the choice in industries where grinding constitutes a major portion of the processing. Typical is a 10 x 34 ft two-compartment mill in closed circuit with an 18-ft diam air separator for cement. Other cement mill sizes are in the order of 12 x 36 ft, 2500 hp; 10 x 37 ft ball and rod (wet), 1400 hp; 13 x 36 ft, 3000 hp; 13 x 40 ft (wet), 3000 hp. Several installations of combination ball and rod mills have been made, and one of the largest is 12 x 45 ft. In connection with the wet grinding of raw materials, the DSM 270-degree screen has been installed in several cement plants with the intention of producing a material finer than 50 mesh. In ore processing, large autogenous mills (121/2 x 20 ft) are being installed.

Jan 2, 1964

By H. Kenworthy, R. B. Fisher, R. G. Knicherbocker, M. M. Fine

The progress made to date in the mineral dressing of complex Arkansas titanium ores is reported in this paper. Concentrates of rutile, a dioxide of titanium, were produced by treating a submarginal ore from the Magnet Cove Rutile Co., Inc., Magnet, Ark. The rutile recovery at present is 45 to 50 pct of the total TiO2, with the possibility of increased recovery with additional research. The work reported herein is part of a general study which will later include results of investigation of other titanium ore bodies in the Magnet, Ark., area. The fragile character of the rutile minerals, the softness of the gangue, the occurrence of pyrite and leucoxene, and the considerable proportion of extremely small size rutile in the presence of montmorillonite- and illite-type clays in the Magnet Cove open-pit mine are the important factors in the mineral dressing of this submarginal rutile ore. History The occurrence of titanium minerals in the Magnet Cove area of Arkansas was recognized as early as 1890, but it was not until about 1912 that any appreciable prospecting for the minerals was undertaken. At that time drilling was begun, a shaft was sunk, and several drifts were driven, but beneficiation to recover the titanium minerals was not attempted. The only successful mining and milling operation of the Magnet Cove rutile deposit was begun in 1932 by the Titanium Corp. of America and continued until 1942. The ore was washed by means of a rotary scrubber and then deslimed in a drag classifier. The discharge was ground in a rod mill, classified, and tabled to recover a rougher rutile concentrate, which was screen-sized and retabled on cleaner tables. The cleaner concentrates were given a reducing roast, screen-sized, and magnetically separated to produce a finished rutile concentrate. Most of the rutile produced during this period was sold abroad. In 1942, the Titanium Alloy Corp. of Arkansas (a subsidiary of the Titanium Alloy Manufacturing Co. of New York) purchased the property and rebuilt the mill. Subsequently, the plant and property were acquired by the Magnet Cove Rutile Co., Inc., of Little Rock, Ark., the present owners. Very little titanium has been produced since 1942. Although the Titanium Corp. activities yielded enough returns to allow continued operation for approximately 10 years, certain factors must be recognized. These are: (1) production of rutile in that period was during a low in the economic cycle which permitted low-cost operation on a small scale, and (2) a considerable portion of the production was above the water level and no drainage problems existed. Prior to this paper there has been no published report of any mineral-dressing investigation of the lower levels of the ore body. Reference is made in another paper1 to an earlier investigation of Magnet Cove rutile by the Rolla laboratory, in which it is stated that recoveries of 12 to 17 pct of the rutile were obtained. The present investigation was undertaken to improve the known milling processes and to provide adequate metallurgical information about the ore treatment. Titanium Technology The titanium mineral of primary interest in the present investigation was the titanium dioxide, rutile. Rutile is one of the industrial minerals whose annual consumption is relatively small but strategically important. The domestic production of rutile was 7100 tons in 1948. The imports of rutile in the same year were approximately 8000 tons.2 A major use of rutile is in the production of welding-rod coatings, for which a product containing a minimum of 92 pct titanic oxide is desired. Other constituents, such as lime, silica, and sulphur, must be held to a minimum, but hard-and-fast specifications for these elements cannot be drawn. It is necessary to incorporate the rutile in a welding-rod coating, make a sufficient number of test welds, and then determine the tensile strength of the weld metal in the as-welded and stress-relieved conditions. Such a test gives

Jan 1, 1950

By G. E. Perry, J. F. Bruskotter, D. G. Russell, J. H. Goodrich

The depletion performance of gas wells has been investigated by mathematical simulation techniques. The gas well model which was studied consisted of a single well located in the center of a bounded, cylindrical, homogeneous reservoir. Dependency of gas compressibility and viscosity on pressure was considered in studies of well performance at both constant mass flow rate and constant flowing pressure conditions. To carry out the investigation, the nonlinear, second-order, partial differential equation which describes Darcy flow of a nonideal gas through porous media was solved numerically. Some of the previous investigations of gas well performance have been of limited general use, because assumptions were introduced to simplify either the gas properties or the basic differential equation. Other studies have been rigorous in these respects but have presented a very limited set of calculated results. The present study was attempted to present a rigorous theoretical model and sufficient numerical results to permit meaningful conclusions to be drawn. It was found that all terms must be retained in the partial differential equation to make accurate predictions. The neglect of higher-order terms, e.g., terms of the order of the "gradient squared", leads to serious material balance errors at large times and to conservative estimates of gas well performance. The higher the gas flow rate and/or the lower the permeability-thickness product of the formation, the more pronounced are these deviations. For example, in a well draining 640 acres in a 25-md-ft formation (8,120 MMcf gas in place) at a constant rate of 993 Mcf/D, the rigorous solution predicts a bottom-hole pressure decline from 4,000 to 1,000 psia in 8.7 years. If higher-order terms are neglected in the differential equation, this decline in pressure is predicted to occur in 5.3 years. With the results of the numerical solution of the differential equation as a basis, simple, easy-to-use approximations for predicting gas well performance for Darcy flow conditions have been developed. These simple approximations are based on the familiar equations for flow of a single, slightly compressible fluid. The approximate methods possess a high degree of accuracy and enable the prediction of long-term gas well performance to be made quickly and accurately without the use of a digital computer. Both transient and stable flow period approximations were developed. INTRODUCTION In recent years income from the sale of natural gas and associated products has represented an ever-incre as ing fraction of the industry's total revenue from operations. To meet the surge in demand for natural gas, the industry has depended heavily upon established reserves and has actively pursued development of new reserves. The search has progressively led to reservoirs which yesterday were too tight and/or deep to yield the desired return on invested capital. More than ever before, evaluation accuracy is now required to forecast the criteria upon which engineering recommendations and management decisions are based. Considerable effort has been expended by both research and operations personnel on the development and application of methods for analyzing and predicting the performance of gas wells. Fundamentally, the problem is the familiar one of extracting data during the drilling, testing and early production life of a well and applying these data within an accurate simulation model to predict long-term behavior. During the past 30 or more years a voluminous literature dealing specifically with gas field problems has been generated. A recent book' lists a comprehensive bibliography of published material through 1959. Over 1,200 references are cited. Since then 39 additional articles on natural gas technology have been published in Transactions volumes of the Society of Petroleum Engineers of AIME. Most existing theory for predicting gas well performance requires that one or more idealizations (e.g., steady-state flow, ideal gas of constant viscosity, small and constant compressibility and constant-viscosity fluid) be applied. Although existing theory may apply directly or be adapted by various artifices to describe specific gas well and reservoir behavior, no widely applicable method is available, and existing methods appear to be subject to appreciable error unless better limits of applicability are defined. The objectives of this paper are (1) to present numerical solutions to the partial differential equation describing gas flow under conditions of general interest in gas well performance prediction work, (2) to present solutions which possess a high order of accuracy for both transient and stabilized flow periods of a well producing at constant rate or constant pressure, and (3) to develop and present simplified relationships which can be used as high-order approximations to the exact numerical results for fast and accurate predictions of gas well performance at the operating level. Combined, these objectives are designed gen-

Jan 1, 1967