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By R. A. Falconer, H. L. Lovell

With increasing requirements for fine coal cleaning and the many advantages of the cyclone operating on a coal-water slurry, a series of studies designed to achieve an enhanced understanding of the cyclone parameters has been pursued. The purpose of this investigation has been to vary a series of dimensional parameters with an experimental 15-in. diam hydro-cyclone, and to determine the relative effects of parameter variations upon ash and sulfur removal. This study of the hydrocyclone is a continuation of a series of investigations, conducted in the Dept. of Mineral preparation at The Pennsylvania State University, which are directed toward the removal of ash and sulfur constituents from fine bituminous coal by size-density separations in cyclones, and toward a fuller understanding of the complex mechanisms involved in such separations. The purpose of this investigation has been to vary a series of dimensional parameters with an experimental 15-in. diam hydrocyclone, and to determine the relative effects of parameter variations upon ash and sulfur removal. Of special interest was the response to cone angle variation, since it is the high included cone angle that generally distinguishes the hydrocyclone as a gravity separator rather than a classifier. DESCRIPTION OF THE HYDROCYCLONE Fig. 1 is a dimensional drawing of the hydrocyclone used in the investigation. The unit was designed and fabricated by Heyl and Patterson, Inc., for experimental use. The dimensional parameters considered were: 1) Three cone sections having included angles of 45, 60, and 95,degrees, 2) Three 3 1/8 in. diam vortex finders having lengths of 15, 17, and 19 1/2 in., 3) Three 4 1/16 in. diam vortex finders having lengths of 15, 17, and 19 1/2 in. 4) Two apex sections having diameters of 2 and 2 1/4 in. The feed inlet orifice had a fixed diameter of 3 in. The hydrocyclone test installation was made at The Pennsylvania State University pilot plant at Barnes-boro, Pa., which operated at 50 tph. During the period that the hydrocyclone was tested, research was in progress at the Barnesboro site to reprocess refuse material from a near-by coal preparation plant in

Jan 1, 1968

By OTTO HERRES

TITANIUM is estimated to be the ninth most plentiful element, ranking after iron, aluminum, and magnesium, and ahead of copper, lead, and zinc. Vast quantities of titanium are widespread throughout the world in ore deposits and beach sands. Before the war, processing plants were operated in England, France, Italy, Czechoslovakia, Norway, Russia, Australia, United States, and Japan. In spite of its widespread occurrence, however, the U. S. Department of Justice has held the titanium industry to be a world monopoly and action was taken in the Federal court during the summer of 1945 to enjoin international patent and marketing agreements and to restore free competition. Possibly the rather surprising lack of public familiarity with this industry of international importance arises from its astonishingly rapid development and growth in the strong hands of some of the greatest chemical companies in the world, including the important foreign companies, Imperial Chemical Industries (British), Montecatini (Italian), I. G. Farben (German), and Titan Kogko Kabushiki Kaisha (Japanese). The rapid growth of the titanium industry in the United States is indicated by a tenfold increase of ore imports in the 1930 to 1940 decade before the war began to affect shipments from overseas. The fact that the industry formerly derived practically all ore for chemical processing in American plants from foreign sources probably also accounts for lack of general public knowledge of titanium. In 1939, to meet the requirements of increasing demand for the white pigment. titanium dioxide, more than 250,000 tons of titanium concentrates moved to this country, principally from the Travancore coast of India where the ilmenite concentrate from the beach sand runs as high as 60 per cent in titanium dioxide. Global warfare put a stop to shipping and thus gave rise to the development of titanium mining on a substantial scale in the United States during 1941.

Jan 1, 1946

Jan 1, 1881

By C. E. Lesher

Two processes for agglomerating fine sized ores with low temperature coke are described. One process (Orcarb) agglomerates ores with limited amounts of carbon; the other (ore-carbon pellets) pelletizes fine sized ores, using low temperature cokes as the binder. Data are presented on the products obtained when taconite, magnetite, and hematite concentrates and several titanium oxide ores were used. REDUCTION of finely divided oxide ores has long been a major metallurgical problem. Various methods of agglomerating, notably briquetting, sintering, nodulizing, and pelletizing, have been developed and are in industrial use. Carbon is the usual reducing agent for oxide ores and attempts have been made to agglomerate fine ores with coking coal in order to get the metallurgical advantages of intimate contact and increased particle sizes suitable for subsequent smelting or reduction.1-3 For the past three years, research has been in progress on two processes for combining fine sized ores with reactive carbon in the form of low temperature coke. By one process, designated Orcarb, the ore is coated with coke carbon in amounts limited to that required for reduction and the result is an appreciable but limited increase in product particle size over that of the original ore. The second process, called ore-carbon pellets, produces pellets of fine ore bound by low temperature coke. The first objective was to develop a process for combining an oxide ore with only enough carbon for its reduction, the amount being that derived from the simple reduction equations. The carbon (that amount theoretically required for the reduction of the oxides in an agglomerate with ore), calculated to CO, ranges from 10 pct for zinc calcines or phosphate ores to 21 pct for rutile and 26 pct for silica. The carbon required for reducing iron oxides falls between the extremes—10 and 26 pct. When the carbon in the agglomerate is low temperature coke, reduction by hydrogen may be expected to take place, thus modifying the calculated carbon require- ment. On the other hand, in practice, an excess of reducing agent over that required in theory is normally used. Screen sizes of three iron ores on which the greater part of the experimental work was performed are given in Table I. Most of the testing was done with Freeport (Renton Mine) coal, but Pittsburgh and Elkhorn bed coals were also used. The first objective was to agglomerate the ore with sufficient low temperature coke to provide carbon for reduction, i.e., in the range from 10 to 25 pct. This was accomplished by preheating the ore, mixing with pulverized coking coal, and completing the coal carbonization in a plain steel rotating retort. The pilot retort, as it is now constituted, is shown by diagram in Fig. 1 and photograph, Fig. 2. Ore is fed into the upper kiln by a screw; it is heated to 900" to 1100°F by direct flame and it is then discharged into an insulating hopper from which it goes

Jan 1, 1956

By Charles White Merrill

A forecast of mineral demand during the remaining years of the 20th century can serve as an excellent starting point for student mining and mineral engineers in planning their professional careers. This approach of appraising demand before seeking supply is not new. of course, but, it is quite the opposite of the traditional attack on mineral resources in which adventurous prospectors, followed by practical miners and engineers, have in the past sought out and developed mineral supply with a faith that markets existed for the products they were preparing to offer. Such faith, even to this day remains fully justified if the product is gold, which still enjoys an unlimited market at $35 a fine ounce, but other mineral products must compete in markets of varying stability and capacity for adsorbing new supply. The world is in a period of rapid expansion. Most basic is the worldwide increase in the number of people which has reached proportions popularly termed "the population explosion." Conservative demographers, noting an increase from 1 ?h billion people at the beginning of the 20th century to 3 billion today, are predicting 5 billion by the year 2000; some predictions are much higher.

Jan 2, 1964

By Daniel C. Jackling

WHAT is written here features some of the things that I would say if I were to de- liver a Presidential address during the Annual Meeting to be held this month in New York. I am aware that custom favors written rather than vocal delivery of such a discourse; and, as this accords exactly with my own preference, I assure readers that they will never be called upon to hear these remarks spoken- anyhow, not by me. My year as President is drawing to a close. As I look back I like to classify and analyze the impressions that have been left with me. It has been a delightful and fascinating experience to me personally; I have appreciated the courtesies and aids, and have been deeply gratified at the honors accorded me. Perhaps the source of greatest satisfaction is the opportunity I have had to sense more about the provinces of this Institute and about the useful functions of the profession that it represents. For 38 years I have been a member. I served two terms as Director-one in 1914-'16 and again in 1927-'29. I have been honored by selection as a Saunders Medalist. I thought I was reasonably familiar with the functions, the ideals, and the activities of the Institute. But the things that I have discerned during the past year have dispelled that conceit. I still think that, a year ago, I was as well informed as most members; but since then I have had the rare privilege of executive service and insight. That has given me a perspective that I feel can be obtained in no other way-as I think the illustrious engineers who have preceded me in office will agree. I wish that I had the power to translate to every member somewhat of the feelings of pride in our organization that a year as President cannot help but instill.

Jan 1, 1939

By C. E. Lesher

Two processes for agglomerating fine sized ores with low temperature coke are described. One process (Orcarb) agglomerates ores with limited amounts of carbon; the other (ore-carbon pellets) pelletizes fine sized ores, using low temperature cokes as the binder. Data are presented on the products obtained when taconite, magnetite, and hematite concentrates and several titanium oxide ores were used. REDUCTION of finely divided oxide ores has long been a major metallurgical problem. Various methods of agglomerating, notably briquetting, sintering, nodulizing, and pelletizing, have been developed and are in industrial use. Carbon is the usual reducing agent for oxide ores and attempts have been made to agglomerate fine ores with coking coal in order to get the metallurgical advantages of intimate contact and increased particle sizes suitable for subsequent smelting or reduction.1-3 For the past three years, research has been in progress on two processes for combining fine sized ores with reactive carbon in the form of low temperature coke. By one process, designated Orcarb, the ore is coated with coke carbon in amounts limited to that required for reduction and the result is an appreciable but limited increase in product particle size over that of the original ore. The second process, called ore-carbon pellets, produces pellets of fine ore bound by low temperature coke. The first objective was to develop a process for combining an oxide ore with only enough carbon for its reduction, the amount being that derived from the simple reduction equations. The carbon (that amount theoretically required for the reduction of the oxides in an agglomerate with ore), calculated to CO, ranges from 10 pct for zinc calcines Or phosphate Ores to 21 pct for rutile and 26 pct for silica. The carbon required for reducing iron oxides falls between the extremes—10 and 26 pet' When the carbon in the agglomerate is low temperature coke, reduction by hydrogen may be expected to take place, thus modifying the calculated carbon require- ment. On the other hand, in practice, an excess of reducing agent over that required in theory is normally used. Screen sizes of three iron ores on which the greater part of the experimental work was performed are given in Table I. Most of the testing was done with Freeport (Renton Mine) coal, but Pittsburgh and Elkhorn bed coals were also used. The first objective was to agglomerate the ore with sufficient low temperature coke to provide carbon for reduction, i.e., in the range from 10 to 25 pct. This was accomplished by preheating the ore, mixing with pulverized coking coal, and completing the coal carbonization in a plain steel rotating retort. The pilot retort, as it is now constituted, is shown by diagram in Fig. 1 and photograph, Fig. 2. Ore is fed into the upper kiln by a screw; it is heated to 900° to 1100°F by direct flame and it is then discharged into an insulating hopper from which it goes

Jan 1, 1956

By C. D. Demond

IN reverberatory smelting, fuel is the chief item of expense, as it commonly is in processes using large percentages of it. Hence the most suitable supply is eagerly sought; that is, the supply which, in the end, yields the greatest net profit. The better grades are not infrequently bought, even at an advanced price, because they are apt to be decidedly more economical. High price, of itself, however, is no merit, for freight is generally the largest part of the cost of fuel, and the nearby supply may yield as high efficiency as that from a greater distance. If a poorer grade is reasonably good, and if its cost is low enough to more than offset the decreased technical efficiency, it is of course the more suitable. Any smelting, operation depends for both efficiency and economy on raising the furnace atmosphere considerably above the "critical" temperature; that is, above the temperature at which smelting is completed. If this temperature is not exceeded, smelting stops, no matter how much coal is burned; and the real value of a fuel depends on the number of degrees that the temperature is continuously kept above this point. For example, if one fuel maintains 2,500° F. and another only 2,100° F., while the "critical" temperature is 2,000° F., the first is worth at least five times as much as the second, although the increase above atmospheric temperature is only one-fifth more in one case than in the other. This "margin of temperature" above the smelting point is much more significant than the total number of heat units developed from the fuel. The case is parallel to that of water flowing from a pipe. The reservoir may contain a billion gallons of water; but, even though the fluid has come to the nozzle, not a drop will run out, where it can be of practical use, unless the level in the reservoir is higher than the nozzle; and the speed and volume of flow depend on how much higher the level is in the reservoir than at this point. If the temperature inn a furnace is not above the critical level there will be no slag to flow over the skimming plate, even though there are enough heat units to bring an unlimited quantity of charge up to the point of slag formation; and just as the value of a water supply for the purpose of putting out a fire depends largely on the effective head, so the difficulties of furnace management

Jan 8, 1914

By H. Stigzelius

FINLAND'S recent mining history is both dramatic and pitiful in its shifting fortunes, dominated as it has been, by the country's proximity to the border zone of opposing dictatorships and social traditions; Fascism to the south, Communism to the east, and Democracy to the west. After 108 years under Russia's more or less harsh rule, Finland gained its democratic independence during the 1917 revolutionary strife in Russia with the official help of Germany and spontaneous help of other neighbors. The young nation was attacked by Russia in 1939 and again in 1941. It is common knowledge how the Finns fought with everything they had and everything they could get against their overwhelming adversary, and how by force of circumstances they landed in the Axis camp in 1941. Finland has never been known as a mining country in the same way as near-by Sweden, whose abundant iron and copper smelters during long periods so greatly contributed to the nation's welfare. Its largely barren, Archaean-granite geology long seemed forbidding. Some mining was done, to be sure; copper and tin at Pitkaranta near the Russian border, and lead and copper at Orijarvi. But towards the end of the last century the absence of a single producing mine cast a pessimistic shadow of truth over the Finnish poet Runeberg's words, that

Jan 1, 1946

By AIME AIME

AT A meeting of the Boston Local Section of the Institute, on Oct. 3, approval was voted to the work done by its representatives on the Committee opposing the passage of a bill by the, Massachusetts Legislature to license engineers. The report is as follows: The Joint Committee on Licensing of Engineers, which included a Committee of the Boston Society of Civil Engineers and representatives of seven other societies,* submitted to the members of the respective societies, on Jan. 8, 1921, a report in which it was stated that on Jan. 4, 1921, a petition was filed in the Legislature of Massachusetts by the Boston Chapter of the American Association of Engineers accompanied by a bill to provide for the registration of professional engineers and land surveyors. This report also stated that at a meeting of this committee, held on Jan. 7, 1921, it was voted:

Jan 1, 1921

AALL,Christian H.,(M '49), Asat.Research Dir , Phosphate Div Monsanto Chem.Co.,Monaanto, Tenn. AAMOT,Olav Crone, (M '29), Dir of Tech., Chromium Min. & Smelt. Co Ltd Box 6215, Hillyard, Spokane, Wash. AARING, Floyd Daniel, (J '48), Prod. Engr., Canadian Gulf Oil Co., 8035 - 102nd St., Edmonton, Alta., Canada AASE, Glenn D., (J '40), Met Engr Western Research Div. ,Amer. Smelt. & Refin. Co., Selby, Calif ABADIE, Henry G (M '43), Senior Prod Engr., Long Beach Oil Dev Co., 255 S Santa Clara Ave Long Beach 2, Calif. ABBOTT,Clarence E (M '04), Civil Engr., 901 Insurance Bldg., Raleigh, N.C. ABBOTT, John, H., (M '46), Resident Mgr., Hickman, Williams & Co., Rm 2205,230 N Michigan Ave., Chicago 1. I11.

Jan 1, 1952

By Kim Beattie

IN spite of the fact that in 1944 Canada experienced a decline in production of all her leading base metals-nickel, zinc, lead, and copper; despite uncured headaches in the coal-mining industry; and cheerfully ignoring a still further drop in gold, the most valuable product of her mines, which had the lowest output of any year since 1931, the Canadian miner retains the traditional optimism of miners everywhere as he looks forward to the postwar period. Some factors should keep the Canadian mining industry from being too optimistic of the coming era of peace, but the fraternity generally holds that its confident attitude towards the future is based on sound reasons. The decline in production in the Canadian mining industry last year can be almost wholly attributed to the serious shortage of labor and the difficulty in obtaining transport and supplies in remote areas. Some falling off occurred in the demand for certain strategic metals, but the diversion of gold miners, especially, without replacements being obtainable, to direct war work or allied pursuits, was certainly the principal cause of the reduced output in 1944. But that is a situation which will right itself at the close of the conflict.

Jan 1, 1945

By H. M. Woodroffe, H. K. Conn, S. J. Rice

World production of asbestos is estimated to be at a current level of almost 3.5 million tons, having more than doubled in the past ten years. A substantial part of the increase has been due to a rapid expansion in the Soviet Union. Production from that country during 1964 is estimated at 1.5 million tons and, as a consequence, Russia has displaced Canada as the leading world producer. Although traditionally the asbestos mining industry has been centered near Sverdlovsk in the Urals, two new producing areas have been under development for some time. It is expected that a new mine will be in operation in 1965 near Kiembi, Kazakhstan, some 300 miles south of Sverdlovsk, and an- other mine at Aktrovak in Tannu-Tuva, west of Lake Baikal. These developments will provide a significant increase in the production capability of Russia. Although internal consumption is expected to increase with the addition of new asbestos- cement producing facilities now under construction in Russia, there is some speculation that exports will also increase.

Jan 2, 1965

By Thomas T., Read

DESIRABLE as it is to summarize what has been set forth in preceding chapters, the task can only be approached with great hesitation. What follows represents the personal views of the author at the moment of writing, reserving the privilege to change them on more mature reflection or in the light of further evidence. With that reservation they may be stated somewhat as follows. Education for the mineral industries falls into two categories; general education and technical vocational, using the word vocational not in its usual sense but to signify preparation for specific activities, in which sense a law school is a vocational school. Even at the beginning, as indicated in the first chapter, mineral industry education was partly general and, partly technical and that relationship still persists, because technical education requires a firm basis of general education. Our general American system is to provide free public' general education through the twelfth grade, or completion of high-school work, though there are already many technical vocational high schools, and even in a community where nearly all the young people are preparing for entrance to college there will be some who wish to qualify for employment at the end of the high-school course, or even on completing junior high. Our educational system, therefore, has not only to provide education for those who intend to proceed beyond the twelfth grade but also for those who, for a variety of reasons, may wish or be forced to cease full-time education at any level between the first and twelfth grades. This study has been chiefly concerned with the problem of what kind and how much technical education to provide for those who have completed the twelfth grade and who wish to make their living in the mineral industries. The obvious fact that the mineral industries employ all sorts of trained persons,

Jan 1, 1941

US 4,190,436 - In the cyanide leaching of gold ore in tailing or ore dump piles, or gold ore in vats or on pads, the ore is agitated and oxygenated by introducing timed bursts of air, along with cyanide in a cyclic or regulated manner. The leach liquor is drained from the material by providing a continuous flow of air. Fines are homogenously mixed, thereby reducing channelling In the ore bed. Yield is improved and cyanide consumption lessened. R M. Hughes Feb. 26, 1980. 7 pp. (75-105). Filed. 12-20-77 (862,335).

Jan 1, 1982

By Robert D. Pike

IN November 1939, on behalf of the Harbison-Walker Refractories Co., the author undertook the study of the problem of utilizing the dolomite of northwestern Ohio for the manufacture of calcined magnesia suitable for use in refractories. Grateful acknowledgment is made of the unfailing assistance and encouragement throughout this work from the executive and technical staff of Harbison-Walker Refractories Company. The dolomite of the Niagara formation that is exposed or near the surface of a wide area in northwestern Ohio1 constitutes a vast supply of almost pure dolomite. It offers a virtually unlimited supply of cheap raw material of uniform dependable analysis for the manufacture of magnesia. A typical analysis of dolomite from the vicinity of Luckey, Ohio, follows: [ ] Brines containing magnesium chloride or sea water can be reacted with calcined dolomite to produce magnesia.2,3 In such reactions the MgCl2 of the brine supplies some of the magnesia and the amount of dolomite required is thereby reduced by an equivalent amount, but brines of commercial importance containing magnesium chloride are some distance away from the purest grades of the dolomite of northwestern Ohio. It was decided therefore to concentrate upon the development of a suitable process for separating the lime and magnesia of dolomite, depend¬ing upon the dolomite itself as the sole source of magnesia. This would make it possible to place a plant at the dolomite quarry, thus eliminating the cost of transporting the stone and also rendering the calcined magnesia available at a most convenient production point, considering the cost of delivery throughout the steel industry. The selection of a process depending solely upon the dolomite as a source of magnesia also necessarily entails production of the lime content of the dolomite as a by-product. It was recognized that if such a lime by-product could be produced in a suitable form, a plant location in northwestern Ohio would also be advantageous for marketing the lime. The problem, therefore, was the discovery and development of a low-cost process for separating the magnesia and lime of the dolomite of northwestern Ohio and producing each in a form relatively free from the other, and meeting the respective requirements of established markets. A satisfactory solution of this problem has been found, and it is the

Jan 1, 1947

By C. K. Leith

THE interdependence of nations in regard to mineral supplies has grown apace with the expanded needs of industry, with depletion of reserves, and with advances in technology. This increased mutual dependence raises many questions of foreign economic policy of special importance in our postwar planning. Realization of the urgent need for the development of a general mineral policy broadly based on national requirements led to discussions of the problem between officials of the Department of State and myself, as a result of which it was suggested that I make an informal and unofficial canvass of the views of mineral specialists of the country on foreign mineral policy.

Jan 1, 1946

By Milnor Roberts

WAR struck the mineral industry of Washington with cross currents that produced a peculiar result. The State's production of coal, industrial minerals, and metals for 1941, valued at $28,507,282, was increased in 1942 under war pressure to approximately $35.000,000. Meanwhile a tremendous demand had arisen for men to construct airfields and many other large projects for the Army and Navy in Washington and Alaska, and Government plants for the mineral industry costing $140,000,000 or more, as well as a call for employees in the U. S. Navy Yard at Bremerton, the sixty shipyards, the four Boeing airplane factories with many auxiliary shops, and hundreds of other plants turning out war materials. In spite of an influx of nearly 300,000 people, causing an increase of 17.1 percent in the population since 1940, according to the Census Bureau, the State clearly is still engaged in an unusual amount of war production in proportion to its population. A large proportion of the workers have been drawn from the mineral industry to the war plants, whether through motives of patriotism, high wages, or, in the Boeing plants at least, the glamour of the operation

Jan 1, 1944

By J. J. Jakosky

The strategic importance of the metallic minerals in our industrial economy, and the declining rates of discovery have focused attention on means of exploration for new mineral deposits. A consideration of exploration techniques leads to an attempt to evaluate the effectiveness of geo- physics as a tool for mining exploration. One means of evaluation will be to compare the use of geophysics in petroleum exploration with its possible uses in mining.

Jan 1, 1949

By A. T. Chatas

A description of the geometrical characteristics of spherical reservoir systems, a discussion of unsteady-state flow of such systems and examples of engineering applications are presented as backgmund material. The fundamental differential equation, a description of average spherical permeability and the introduction of the Laplace transformation serve as theoretical foundations. Engineering concepts are investigated to indicate particular solutions of interest, which are analytically obtained with the aid of the Laplace transform. These are numerically evaluated by computer, and presented in tabular form. INTRODUCTION A tractable mathematical analysis of unsteady fluid flow through porous media generally requires incorporation of a geometrical symmetry. The simplest forms include the linear, cylindrical (radial) and spherical. Most analytical endeavors have concentrated on cylindrical symmetry because it occurs more often in petroleum reservoirs. Nevertheless, some reservoir systems do exist that are better approximated by spherical geometry. Review of technical literature revealed but a single reference to unsteady spherical flow in petroleum reservoirs.l The motive and purpose of the present work was to remove this gap in technical information, and to provide the practicing engineer with some useful analytical tools. The mathematical details associated with the particular solutions of interest involved use of the Laplace transformation. Hurst and van Everdingen previously demonstrated the efficacy of this operational technique, and in many respects the present treatment was patterned after their earlier work.2 PRELIMINARY CONSIDERATIONS GEOMETRICAL CHARACTERISTICS Geometrically, a spherical reservoir system is defined at any instant of time by two concentric hemispheres whose physical properties of interest vary only with the radial distance. Every physical property is thus restricted to be a space function of only one variable: the distance along a radius vector emanating from the center. Such a system is composed of an outer region and an inner region, separated by a defined internal boundary. The inner region simply extends inward from this boundary, whereas the outer region extends outward from it to an external boundary. The position of the internal boundary is presumed fixed, so that the size of the inner region remains constant. On the other hand, the position of the external boundary at any given instant of time is determined by the distance into the system that a sensible pressure reaction has occurred, Thus, the external boundary may change position with time. It initially emerges from the inner region and advances outward to its ultimate position. When this ultimate position coincides with a geometric limit, the reservoir system is said to be limited. When it coincides with points subject to pressure gradients furthest removed from the internal boundary, yet short of a geometric limit, the system is said to be unlimited. In this investigation two different boundary conditions are imposed at the ultimate boundaries of limited systems. The first requires that no fluid flow occur across this boundary; the second that the pressure remain fixed at this boundary.3-5 UNSTEADY-STATE FLOW In a strict sense virtually all flow phenomena associated with a reservoir system are unsteady-state. The transient behavior of these phenomena requires accounting, however, only when time must be introduced as an explicit variable. Otherwise, steady-state mechanics may be used. Analytically, steady-state conditions prevail in a reservoir system only over that portion of its history when this relation is satisfied:

Jan 1, 1967