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By R. R. Kimpel, L. G. Austin

An equation is derived describing fragment size for single fracture of brittle solids. It contains the equations of earlier workers as special or approximate cases and, in addition, is capable of describing coarse distributions in which a few large particles are produced on fracture. The equation can be fitted well to single fracture experiments where over-breakage is avoided. In 1956 Broadbent and callcottl described a method of analyzing the unit operation of grinding, applicable to homogeneous breakage of brittle materials. In essence, the grinding process was split into two parts: 1) the fractional amount of a given size which is selected for grinding per unit time, 2) the size-weight distribution of the fragments produced by breakage of this certain size (primary breakage distribution function). The theory was formulated using matrix algebra. They attempted an experimental verification of the theory using an assumed primary breakage distribution but the results were not very satisfactory. Austin and Gardner2 showed that this assumed distribution was widely different from experimental values and that it led to the poor agreement of predicted size-weight distributions with experiment found by Broadbent and Callcott. In addition, Austin and Gardner2,3,4 reformulated the original approach in terms of differential equations of grinding and demonstrated that the approach led to a very satisfactory description of the grinding process, providing that the descriptive parameters were measured experimentally. Recent work5 has substantiated these findings and the distribution functions of several materials ground under different conditions in different mills have been determined experimentally. The fraction underweight versus size used by

Jan 1, 1965

By AIME AIME

ARRANGEMENTS for the Annual Meeting of the Institute were well advanced at the end of December as the following program will show. Heretofore this has been printed separately, but its inclusion in the Annual Review issue of MINING AND METALLURGY will, it is hoped, make it more easily available for reference until the final program is issued, which will be distributed at the meeting. Added details will appear in the February issue. Last year's meeting drew a record crowd of over 2300 which should be exceeded this year. Early reservations at the headquarters hotel, the Waldorf-Astoria, or any other convenient hotel are desirable, as are prompt reservations for the Annual Dinner. No one need worry about too much speechmaking this year, for the honors will be awarded and accepted in a few words instead of a few paragraphs, in seconds rather than minutes.

Jan 1, 1939

By David Baker

Our large modern blast-furnaces, equipped with ore-bins, larries and mechanical means for putting stock into storage, withdrawing it therefrom, and charging it at the tunnel-head, are indeed wonderful in capacity; yet, it is admitted that, with some notable exceptions, they have disappointed us in economy—that is, in the items of low fuel-consumption, uniformity of product, freedom from slips, and reduced cost of repairs and relining. The manager who estimated the cost of pig-iron to be made in a modern plant, by taking the costs of the hand-filled furnace and deducting the amount to be saved by the mechanical appliances, has been surprised, in many cases, to find that unfavorable results in these items of economy have greatly reduced his expected gains. Is there any reason why the fuel-consumption should be greater for a modern furnace than for an older stack using the same mixture ? Certainly the equipment is much more complete, and the trouble, therefore, must lie in the management or in the character of that equipment. Everybody knows that intelligent and vigilant management is a prime requisite: that any neglect of a detail, though it may not be felt that day or week, will surely sooner or later make its appearance as an increased item of cost. But to hold the furnace-maaager responsible for the relatively poor work of the modern blast-furnace would be, I am convinced, a great injustice. For its management has received much more study and care than was given to the older types. Many furnace-managers have lost their health through worrying over this problem, and some hare lost their positions, being held responsible for results made inevitable, as I believe, by the equipment provided for them.

Jan 1, 1905

Jan 1, 1968

Jan 1, 1968

By A. U. Seybolt

The solubility of oxygen in a iron has been determined in the range between 700° and 900°C. The solubility is a function of temperature and varies from about 0.008 pct oxygen at 700°C to atureandabout 0.03 pct at 900°C. The heat of solution is approximately +15,500 cal per mol. AS pointed out in a recent paper by Kitchener et al.,1 there has been a lack of agreement among many investigators even as to the order of magnitude of the solid solubility of oxygen in the various forms of iron. This lack of agreement is attributable in large part to the difficulties in the determination of a small oxygen solubility; but because the problem has remained so long unsettled, it also indicates a lack of interest which is rather surprising when the demonstrated importance of small amounts of soluble nonmetallic impurities in iron is considered. The work of Kitchener et al. apparently leaves the solubility of oxygen in iron in a satisfactory state, but no attempt was made to investigate the solubility in a iron. The solubility of oxygen in a iron is actually of greater interest, since it is in this form that iron and mild steels are employed ordinarily. That the effect of oxygen in iron is of more than theoretical interest has been well established by Fast,' and more recently by Rees and Hopkins," who demonstrated that oxygen in the range between 0.0008 and 0.27 wt pct has a pronounced effect upon the mechanical properties. Previous Work and Methods Used To report in detail the literature relating to the solubility of oxygen in a iron would require an inordinate amount of space. For those interested in reviewing this work, a bibliography4-13 of the more significant papers is appended. In general, two methods of studying this problem have been used. One is the gas-metal equilibrium method where the H2O-H2-Fe or the CO2-CO-Fe equilibria have been used. The other is the more direct approach of the oxidation of thin strips of pure iron by packing in mill scale or by air or gaseous oxygen at some desired temperature. In this method oxygen is allowed to oxidize the surface and then to diffuse inward until saturation is obtained. In the gas-metal equilibrium method the oxygen dissolved in solid iron at a given temperature is proportional to the ratio of the water vapor-hydrogen pressures or the CO2-CO pressures over the sample for small ratio values. If the ratio becomes higher than a critical value, then an oxide phase makes its appearance (the solution becomes supersaturated). In principle, it is possible to use a series of H2O/H2 or CO2/CO ratios and to find by analysis the corresponding amounts of oxygen in solid solution at constant temperature. At the point where a very small increase in the gas ratio (increase in oxidizing powder) produces a large increase in oxygen content, the solid solubility limit is reached. Alternately, if the critical ratio is known, it is possible to use the procedure of Kitchener et al.1 and to use a ratio which is near but below the critical one. The solubility corresponding to this lower ratio will not be the saturation solubility at the temperature employed, but the saturation solubility can be calculated by multiplying the measured solubility by the critical ratio over the ratio used. However, in the case where oxygen gas is the oxidizing medium, the saturation solubility is not a function of pressure, providing the pressure exceeds the dissociation pressure of FeO in equilibrium with iron. This is 1.2x10-16 mm at 800 °C, according to Dushman." As pointed out by Darken17 in discussing the FeO phase diagram, most of the possible errors tend to yield high values of oxygen solubility. For example, one circumstance which evidently caused the reporting of many high values was the use of finely divided or powdered iron in the gas equilibrium method. Because of the large surface area of such a sample, and the likelihood of some surface contamination if only by exposure to air, the results tended to be high. The direct oxidation method which was used in this work has the advantage in that it is simple and direct, but it suffers from one disadvantage: equilibrium can only be approached from the low oxygen side. The important factors to be kept under control are the following: 1—use of high purity iron to avoid internal oxidation (oxidation of readily

Jan 1, 1955

By Arthur Phillips

The progress made in recent years in the art of dispersion-hardening has naturally led to an intensive study of alloy systems capable of yielding supersaturated solid solutions at ordinary temperatures. In general, the investigations have been confined to rather precise determinations of solubility limits and to experimental approaches designed to furnish more complete information regarding the rate and nature of precipitation under appropriate thermal conditions. Efforts are being made to focus more sharply on the atomic changes that are a direct consequence of the instability of the supersaturated solution. Here precision X-ray methods have come to be of considerable importance because lattice parameter measurements indicate very precisely the concentration of solute atoms in the solvent lattice. In spite of the general acceptance of parameter values as a criterion for the placing of solubility limits, it may be suggested that no thorough appraisal has been made of the several factors that conceivably may affect such measurements. More specifically, little attention has been devoted to the significance of surface energy conditions, specimen size and method of preparation, with particular regard to the genesis of the grains and the surface concentration changes as a consequence of heat treatment and etching. Stenzel and Weertsl recently published the results of a detailed study of precipitation reactions in aluminum-rich copper alloys. They found that, although copper lowers the lattice constant of aluminum, a 5 per cent copper alloy quenched from 150" and 225' C. had parameter values unquestionably higher than that of pure aluminum. Their results seem to substantiate, at least qualitatively, the earlier work of von Göler and Sachs,2 who indicated a parameter value, for the same alloy annealed for 24 hr. at 200° C., some 0.0008Å. larger than that of pure aluminum. Stenzel and Weerts attributed the abnormal lattice dimension to the effect of strain induced by the precipitation of CuA12. Weerts3 later

Jan 1, 1934

By W. M. Myers

MINERAL Economics is the most recent profession to be recognized as a separate division of the mineral industries. It has originated from the increasing awareness of the importance of the economic aspects of industries concerned with discovery, extraction, and utilization of minerals. It is concerned with the interrelated fields of economics and technology. The individual trained in economics alone cannot qualify. The curriculum in the School of Mineral Industries at The Pennsylvania State College was approved in May 1946, and enrollment begun in September of that year. Due to the transfer of advanced students from other courses, particularly metallurgy and electrical engineering, it was possible to graduate the first seniors in June 1947. The next class was graduated in February 1948. From experience derived from placing these graduates in industry, and from information supplied by prospective employers, valuable data have been obtained in the organization and operation of the course of study.

Jan 1, 1948

By William J. Priestley

Much time has been devoted, by metallurgists, to the study of steel after solidification and remarkable strides have been made in the heat treatment of steel, but less knowledge is available of the thermophysical activity of the constituents of steel prior to solidification in the mold. It is known that certain elements added to steel produce marked changes in physical properties, also that other elements added to steel produce similar changes, but we have only meager knowledge as 'to. how these elements combine in steel under different conditions of solidification. It is not sufficient to know, from chemical analysis, that a certain element is present in steel. We should know how this element is in combination with the other elements and whether the combination is such as will give the greatest physical properties. Certain elements go into solid solution with the iron, while others segregate to the grain boundaries and combine with the impurities collected there. Until it is known where an alloy produces the most beneficial effect and a means is determined for controlling its physical location by altering solidification conditions, or otherwise, we will not obtain the maximum value from our alloys. When molten steel freezes, it forms a heterogeneous mass of various crystalline constituents; and as the transformation of steel from a liquid state to the solid crystallized state is a critical step, involving as great a transfer of heat as any other operation in the making of finished steel, a variation in the rate of this heat transfer will have much to do with the arrangement of the various constituents in the solid state. The object of this paper is to show some of the effects on steel caused by variations in the rate of cooling in the ingot mold, particularly as to ingotism, segregation, dendrites, and intergranular material.

Jan 1, 1924

By John B. Hastings

THE reconnaissance of the Goldfield mining-district, described in this paper, was made in May and June, 1905, and, though this time was too short for a complete report, the work accomplished may serve as a basis for more thorough future research. Dr. Berkey has examined the rocks collected by myself, and I am using his classifications. As a result of further field-work, and Dr. Berkey's examination of the rocks, this paper is an elaboration and correction of my views expressed in the Gold-field Sun, May 12, 1905. The sketch-map, Fig. 1, illustrates the geology of the Goldfield mining-district. Goldfield is an eruptive complex, consisting of alaskite (binary granite), hornblende-andesite, hornblende-dacite, rhyolite, pyroxene-andesite, pyroxene-dacite (sometimes containing, a small quantity of olivine), quartz-felsite, olivine-pyroxene-ande¬site, and basalt. Considering this list to be arranged in the order of eruption, the age-sequence of the rocks conforms to Richthofen's law, formulated in 1868. From his observations in Europe and America, propylite, andesite, trachyte, rhyolite and basalt, occurring together, succeed one another. In a general way, the medium and more acidic rocks precede the most asic-a result supposed by some to have arisen from their relative position beneath the surface, and due to a rude stratification by gravity in the original cooling magma during the older history of the earth, or to the same differentiation occurring during a quiescent (molten ?) period preceding eruption, being aided by the ease with which acidic rocks, mixed with water vapors, become fusible. In effect, the more basic and less re-

Mar 1, 1906

By H. J. LONGMORE

MORE improvements have probably been made in the diamond-drill field in the past decade than were accomplished in the entire prior period since diamond drilling was discovered in 1864 by a French engineer named Leschot. True, machines were improved, and new accessories were adopted from time to time up to 1929, but no radical changes were made. The basic principle instituted during the early years of the industry were still in use in 1929. At that time, practically the only diamonds used were "black diamonds" or "carbon." These came from Brazil through a rather round- about route, and by the time they got to the drilling trade their cost was excessive-$175 per carat and even higher at the peak. Perhaps because of this. or perhaps because of increased competition, the industry sought ways to reduce expenses even in the face of constantly increased labor costs due to higher wages and reduction in hours worked. The solution seemed to rest in two things-use of a cheaper cutting medium to replace the carbon diamond and the development of new machines to drill faster and thus produce more hole per shift of operation.

Jan 1, 1940

By AIME AIME

COAL preparation will be the main topic discussed at the first fall meeting of the Coal Division at Pittsburgh, Sept. 11, 12 and 13, though valuation, mergers, safety, stream pollution and other topics will not' be neglected. It is particularly appropriate that the great changes taking place in preparing coal for the market should be discussed at length where in the plants of the Pittsburgh Coal Co. and others the opportunity is afforded to see on a large scale just what is being accomplished. In wartime, the United States broke all records in coal production, but, as the late Franklin K. Lane pointed out, every fifth car shipped consisted of dirt. Obviously that constituted a big bur- den on industry and, in the remaking of the business which is now taking place both in the anthracite and bituminous fields, clean coal has properly enough be- come a watchward. Central coal-cleaning plants are being erected as a part answer to the puzzled inquiry of those familiar with metal mining as to why miners of coal have so long been content with what are relatively small units of production. Gradually big collieries comparable in tonnage output to the biggest copper mines are being built, and excellent examples are to be seen near Pittsburgh. Even the age-long tradition of the coal operator in favor of the single shift is

Jan 1, 1930

(Members are urged to send in for this column any notes of interest concerning themselves or their fellow-members.) Members and guests who registered at Institute headquarters during the first half of March: James C. H. Ferguson, San Francisco, Cal. Capt. A. F. Lucas, Washington, D.C. Henry Adams, Stamford, Conn. Dexter P. Cooper, New York, N. Y. H. A. Wheeler, St. Louis, Mo. L. D. Moore, Chatham, N. J. John M. Sherrerd, Easton, Pa. Hennen Jennings, Washington, D. C. R. T. White, formerly General Manager of the Braden Copper Co., Chile, is to take charge of a copper company in Caucasus, South Russia.

Jan 4, 1914

By Dexter Kimball

THE ease and promptness with which the public as a whole becomes accustomed to and takes advantage of the work of the engineer, using the term in a broad sense, is almost startling. Surprise at, and fear of radical innovations in transportation and private service quickly give way to blasé indifference, followed instantly by all manner of criticism that these things are not better constructed and managed. Does the street car stop a few minutes on a switch?-summon the State Commission. Is the Overland Express fifteen minutes late on a three thousand mile run?-Congress is memorialized to make the great railroad companies attend to their business. Does central not respond instantly when we take down the telephone receiver?-anathema!! Do the electric lights go out for a minute or so?-the darkness is illuminated by caustic sarcasm and other kinds of spoken English consigning all engineering and engineers to perdition; everyone apparently forgetting how steep the hills were before the days of street cars, how far away San Francisco was before the days of the locomotive, the telegraph and telephone, and how difficult it must have been to study by the light of a tallow candle.

Jan 9, 1922

By Vaughn Moyer

A method for incorporating well drawdown effect into reservoir calculations is presented in detail, together with examples of its use for widely divergent conditions that could be normally encountered in oil reservoir sands. Tentative conclusions as to the effect such factors as permeability, producing interval, well spacing, or well damage caused by completion or repair practice could have upon economic ultimate recovery are reached. It is carefully pointed out that the conclusions reached are subject to limitations indicated in the text, and placed upon all calculations made in the paper. Introduction Papers have been presentedl-3 in which theoretical depletion histories for reservoirs under equilibrium conditions and no appreciable well-bore drawdown pressure are determined. However, except for a limited number of cases, appreciable drawdown Pressures in a well bore exist, and Pressure and saturation gradients consequently vary throughout a reservoir. This Paper is an attempt to incorporate well-pressure drawdown into reservoir history, and to analyze certain factors, such as those involving recovery, well spacing, and productivity index, from the standpoint of permeability and drainage radius. BY incorporation of drawdown into reservoir history, it is believed that theoretical considerations will more closely approxi- mate actual reservoir behavior experienced in an oil field. For purposes of simplification, a solution gas-drive type field1 without primary gas cap, has been selected. Basic Data and Assumptions Details of equilibrium saturation conditions for no drawdown production for various pressures in a reservoir are deter-minable by methods described by several are permitting the construction of a curve of oil saturation vs Pressure for any selected combination of initial interstitial water and hydrocarbon saturation (Fig I). This curve is then a description of equilibrium saturation conditions at any given pressure in a reservoir. Developing the above, details of saturation and flow permeability may thus be determined for any increment or portion of a well drainage area or reservoir. In this manner the effect of pressure differential (drawdown) may be incorporated into reservoir and well drainage considerations. It is pointed out that this method thus makes use of no-drawdown equilibrium production data, superimposing a draw-hwn effect upon them. It also assumes that net flow conditions in any considered increment of reservoir are not materially altered by the entrance of fluids from other increments into them, but approach equilibrium for the existing pressure and saturation (i.e., each increment behaves in more or less independent fashion, dependent largely upon the equilibrium considerations mentioned above)

Jan 1, 1948

By Vaughn Moyer

A method for incorporating well drawdown effect into reservoir calculations is presented in detail, together with examples of its use for widely divergent conditions that could be normally encountered in oil reservoir sands. Tentative conclusions as to the effect such factors as permeability, producing interval, well spacing, or well damage caused by completion or repair practice could have upon economic ultimate recovery are reached. It is carefully pointed out that the conclusions reached are subject to limitations indicated in the text, and placed upon all calculations made in the paper. Introduction Papers have been presentedl-3 in which theoretical depletion histories for reservoirs under equilibrium conditions and no appreciable well-bore drawdown pressure are determined. However, except for a limited number of cases, appreciable drawdown Pressures in a well bore exist, and Pressure and saturation gradients consequently vary throughout a reservoir. This Paper is an attempt to incorporate well-pressure drawdown into reservoir history, and to analyze certain factors, such as those involving recovery, well spacing, and productivity index, from the standpoint of permeability and drainage radius. BY incorporation of drawdown into reservoir history, it is believed that theoretical considerations will more closely approxi- mate actual reservoir behavior experienced in an oil field. For purposes of simplification, a solution gas-drive type field1 without primary gas cap, has been selected. Basic Data and Assumptions Details of equilibrium saturation conditions for no drawdown production for various pressures in a reservoir are deter-minable by methods described by several are permitting the construction of a curve of oil saturation vs Pressure for any selected combination of initial interstitial water and hydrocarbon saturation (Fig I). This curve is then a description of equilibrium saturation conditions at any given pressure in a reservoir. Developing the above, details of saturation and flow permeability may thus be determined for any increment or portion of a well drainage area or reservoir. In this manner the effect of pressure differential (drawdown) may be incorporated into reservoir and well drainage considerations. It is pointed out that this method thus makes use of no-drawdown equilibrium production data, superimposing a draw-hwn effect upon them. It also assumes that net flow conditions in any considered increment of reservoir are not materially altered by the entrance of fluids from other increments into them, but approach equilibrium for the existing pressure and saturation (i.e., each increment behaves in more or less independent fashion, dependent largely upon the equilibrium considerations mentioned above)

Jan 1, 1948

By F. M. d’Heurle

Films of molybdenum have been prepared by sputtering onto oxidized silicon substrates. The resistivity. lattice parameter, orientation, and grain size were studied as a function of substrate temperature and substrate bias. Under normal sputtering conditions, the resistivity of the films was found to be quite high (600 x 10 ohm-crn). However, with the use of the negative substrate bias of 100 v and a substrate temperature of 350°C, films weve produced with a resistivity of ahout twice that of bulk molybdenum. The lattice parameters measured in a direction nornzal to the surface of the films weve found to be gveatev than the bulk value. This was interpreted as being at least partly due to the presence of compressive stresses. The effects of annealing in an Ar-H atmosphere were studied in terms of diffraction line width, lattice parameter, and resistivity. BECAUSE of its relatively low bulk resistivity (5.6 x 106 ohm-cm)' molybdenum is potentially interesting as a thin-film conductor in integrated circuits. An additional feature which makes it attractive for this purpose is its low coefficient of expansion (5.6 x KT6 per "c),' which is fairly well matched to that of silicon (3.2 x 10 per c). It is possible to deposit molybdenum films by evaporation but generally films produced in this manner have a high resistivity. In order to achieve resistivities close to bulk value, Holmwood and Glang found it necessary to operate in a vacuum of about 107 Torr and to maintain the substrates at 600 C during film deposition. Sputtered molybdenum films have been examined by Belser et a1.7 and, recently, by Glang et al.' This paper describes the results of an attempt to extend some of that work and examine the effects of annealing and getter sputtering on the physical and structural properties of the films produced. SPUTTERING APPARATUS AND PROCEDURE The apparatus used for most of the film sputtering work described here consisted of two "fingers" serving as anode and cathode, respectively, which were mounted within an 18-in.-diam glass chamber. A liquid nitrogen-trapped 6-in. diffusion-pump system was used to achieve a vacuum of about 1 x 107 Torr within the chamber prior to sputtering. The essential features of the equipment are shown in Fig. 1. Cathode and anode fingers are stainless-steel tubes isolated from the top and bottom plates by Teflon collars. In order to limit the discharge to the space between anode and cathode, each finger is surrounded by an aluminum hield, at ground potential, having an internal diameter 18 in. larger than the outside diameter of the finger. The cathode and anode fingers are 6 and 4 in. in diam, respectively. A 116-in.-thick sheet of molybdenum is brazed with a 10 pct Pd, 58 pct Ag, 32 pct Cu alloy to a copper disc which is mounted by means of screws and a large 0 ring onto the lower end of the cathode finger. The disc is cooled during sputtering by water circulation inside the finger. The use of several feet of plastic tubing for the water input and outputg reduces leakage to ground to less than 1 ma when the cathode potential is raised to 5 kv. The upper end of the anode finger is terminated by a brazed-on copper block. A variety of specimen holders can be easily mounted on the upper face of this block. Substrate heating or cooling is achieved by use of an appropriate unit attached to the lower face of the same block. Heating is achieved by means of cartridge-type heaters and cooling by copper coils fed with forming gas under pressure. The inner chamber of the specimen finger constitutes a small vacuum chamber of its own which is evacuated by an auxiliary mechanical pump in order to limit heating element oxidation and heat transfer by convection currents. An advantage of the finger arrangement is the absence of cooling and heating coils and wires within the main chamber. The stain less-steel shutter is useful to establish a discharge for cleaning the cathode at the beginning of each sputtering run. Water cooling of the shutter reduces heating and the out-gassing of impurities which might condense on the nearby substrates. Unless otherwise specified, the substrates used in these experiments were 1-in.-diam oxidized silicon wafe:s, 0.007 in. thick, having an oxide thickness of 6000A. The substrate holders were large copper discs onto the surface of which a number of molybdenum discs, 116 in. thick and 78 in. in diam, were brazed. The wafers were clamped to the molybdenum discs

Jan 1, 1967

By L. T. Stanley

A method is described whereby the behavior of the front is approximated when gas is injected into a thick reservoir having reasonably homogeneous properties. The method is applied to the Abqaiq field of Saudi Arabia. The producing member is the Arab-D, a high-permeability calcarenite which has no continuous betlding planes. Field performance indicates the injected gas to be partially miscible with the reservoir oil because gas volume factors experienced are lower than those predicted by the gas law. Eqlrilibril~m calculations confirnz ihis and also show that the volume factor may vary appreciably, depending on the relative quantities of oil and gas in contact in the reservoir; consequently, volutnetric balances are made for the purpose of determining the behavior of the gas volume factor during injection history. The effect of gravity segregation on position and shape of the gas front is approximated by dividing the producing section into three zones vertically and tracing the movement of the average interface in each zone, with counterflow of oil and gas taking place betweell zones behind the front. This results in a gas front that advances more rapidly along the top of [he formation than along the base, producing an "umbrella" effect in cross section that becomes more pronounced as the front progresses. The calculations cover the gas-injection period of Abqaiq field history through 1958, and the position of the gas front is plotted at one-year intervals. Finally, some comparisotls between the calcrlated fronial position and the gas-oil contact as Measured by neutron logs are made. INTRODUCTION Fig. 1 is a structure contour map of the Abqaiq field. For analytical purpcses, the field has been divided into two areas designated A and B, as shown on the map. Gas injection into Area A was begun in early 1954 into two wells located near the crest of the structure on the north-south axis of the anticline. During the period covered by this paper, the average injection rate has been 122 MMscf/D with a maximum sustained rate of 160 MMscf/D. The reservoir pressure has been maintained at 2,450 psig since start of gas injection. The reservoir originally was undersaturated but, prior to pressure maintenance, the pressure was drawn below the bubble point in most of the Area A section, creating an in-place free-gas saturation of 8 per cent at the crest of the structure. The average critical gas saturation is 13 per cent established by laboratcry core tests. That the entire reservoir remained below critical gas saturation prior to gas injection is borne out by the fact that none of the crestal wells have exhibited high gas-oil ratios during production history. The Area A reservoir is a carbonate section about 200-ft thick having average porosity and permeability of the order of 22 per cent and 500 md, respectively. The productive horizon is the Arab-D member of Jurassic age and is encountered at an average depth of

By Julian Szekely

Through the simultaneous statement of Maxwell's equations. the turbulent Navier-Stokes equations and the differential thermal energy balance equation, a mathematical representation has been developed for heat transfer and fluid flow in electric arc furnaces. In broad outline the theoretical predictions appear to be consistent with experimental measurements. A discussion is presented of the general arc furnace control and optimization problem, together with the potential for the incorporation of the mathematical model given in the paper, into future control and optimization schemes. ELECTRIC ARC FURNACE STEELMAKING accounts for about 24% of the total steel produced in the U.S., consuming about 550kw-hr/ton of steel which amounts to about 1.4x1010 kw-hr annually. The percentage of steel produced by the electric arc furnace route has doubled since 1960 and is expected to increase further in the foreseeable future, particularly with the more extensive use of direct reduction technology. Table I shows, in terms of percentages, the principal items that contribute to the cost of running an electric arc furnace. It is seen that in addition to the fixed costs (labor, depreciation, taxes etc.) electrode costs and power consumption are the dominant inputs, and it follows that process changes that would ultimately reduce any of these cost components would have a significant impact on the efficiency of the operation. There are three main areas where progress in arc furnace design and operation must be directed in the next decade (Committee on Technology, 1981). 1. Increased furnace productivity 2. Reduction in processing cost 3. Improvement in the thermal efficiency of the furnace An estimate of the current operating efficiency of the electric arc furnaces may be obtained by comparing the theoretical minimum energy consumption per ton of steel with those achieved in operational practice. Theoretically 330-360 kw-hrs of electricity are required to melt one ton of cold scrap. For superheating, 8-12 kWh per 100°F are required. The actual energy requirements are given in Table II. It is seen that furnaces currently operate at 70-80% efficiency, with the major heat loss from the furnace resulting from the waste gases (Committee on Technology, 1981). While it is apparent that operational experience has produced a technology that is reasonably energy efficient this has been achieved in the almost complete absence of any detailed knowledge concerning the fundamental heat transfer mechanisms occuring in the furnace. The purpose of the present paper is to present a case for the usefulness of mathematical models in increasing the thermal efficiency of furnaces by investigating these heat transfer mechanisms and then combining this knowledge with existing electrode regulator mechanisms to produce truly efficient power cycles for melting and refining. In particular, existing mathematical models describing convection, radiation, and electro-magnetism in the furnace should be employed, and the development of optimization models which balance the cost of electrodes and energy against the thermal efficience of the furnace should be undertaken. Recent work in this laboratory (Szekely, McKelliget, 1981, 1982, 1983; Szekely, McKelliget, Choudhary, 1983) has made a useful start towards solving the problem of heat transfer within the electric arc furnace but the work still needs to be directly related to existing furnace power cycles and tested against plant scale measurements.

Jan 1, 1984

By A. Lubinski, C. R. Stewart, K. A. Blenkarn

Storage porosity has been considered one of the important pore geometry characteristics of heterogeneous-porosity limestones. Storage pores are only containers for fluids, in contrast to flow channel pores which both contain fluids and provide continuity for fluid flow. The concept of another geometry characteristic, "poro-striction", is presented as a second pertinent variable in describing limestone pore space. In simple terms, poro-striction is a measure of the flow resistance between storage and flow channel pores. Alternating-flow core-testing theory provides flow relationships which can be used to divide the pore space of heterogeneous-porosity media into flow channel and storage pores and to measure the "porostriction" of the latter. Experimental application of this theory to naturally occurring heterogeneous limestones shows that "porostriction" and the ratio of storage to flow channel pores can be estimated. Porostriction and porosity ratio are microscopic characteristics which should influence oil-recovery efficiencies during certain types of displacement processes. A knowledge of pore geometry should be valuable in designing or selecting the most effective oil-recovery process for heterogeneous limestones containing storage porosity. INTRODUCTION The primary and secondary recovery of oil from limestone (carbonate) reservoirs has been and will continue to be a major source of the world's supply of petroleum. Oil recovery from this type of formation is strongly influenced by the size, shape and arrangement of the pore spaces which hold the formation fluids. Therefore, it is expected that better knowledge of pore geometry would lead to design of more effective recovery processes. The concept of storage and flow channel pores has been presented as an important characteristic of limestone porosity.1 In this concept, storage pores are only containers for fluids, whereas flow channel pores are those pores which both contain and transmit the fluids. The work reported herein involves the concept of an additional pore characteristic called "porostriction". This characteristic can be visualized as the flow resistance between the storage and flow channel pores. This resistance is an important pore geometry characteristic because it determines how easily gas and oil can replenish fluids removed from the flow channel pores. Fatt and co-workers at the U. of California have studied the effect of storage porosity and a factor similar to porostriction on transient-flow response of models of porous media during a pressure build-up or drawdown test.55 These models consisted of porous sandstone cores with artificially simulated storage pores. It is the purpose of this paper to describe tests which permit the storage porosity and porostriction of actual reservoir core samples to be estimated. The tests used for this purpose involved not transient tests but, rather, an alternating-flow technique in which pressure and flow are varied according to a sine-wave relationship. This technique may offer advantages over transient methods. THE POROSTRICTION CONCEPT Before discussing alternating-flow (A.F.) tests in core samples, it is necessary to define the porostriction parameter. For this purpose attention is focused upon an elemental volume v representative of a porous medium having both flow channel pores and restricted-access storage pores. For such an elemental volume, it is considered that the storage porosity is combined to form a single pore and that the access into the storage porosity may be represented by a single capillary tube connecting the single pore to the flow channels of the elemental volume. Let the radius of the capillary tube be designated as Rc and its length as L,. When fluid flows into or out of the pore, the following equation (Poiseuille's law) relates flow rate q to pressure drop p, and the physical characteristics of the tube and the fluid of viscosity jx.