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By H. W. Graham

THE young metallurgist of today who thinks casually of the technical literature of the steel industry might conclude that little has been published concerning the Bessemer process. This conclusion is true as relating to the last decade or two, but there is a fairly voluminous Bessemer literature in the period of 1860 to 1910, Since that time, however, an entirely new level of metal-lurgical knowledge of steelmaking has been reached; and the present paper is simply an effort to look broadly from this new level and to bring the recorded history of the process up to date, It is an effort to appraise the acid Bessemer method of steelmaking in the light of today's technical knowledge thereof. In this paper matters of history will be dealt with only insofar as they contribute to an understanding of today's situation. Attention will be directed to the apparent causes of past developments in seeking to perceive the true direction of trends now in existence and effective as bearing upon future developments. The paper will discuss the economics of the Bessemer process, but only to the extent that will bear upon the metallurgist's understanding of his respon-sibility. The problem of the quality of Bes-semer steel will be reviewed and examples will be given of the technical data upon which the reasoning of the paper is based, Matters of engineering design, mechanical maintenance, operation and metallurgical investigation will be surveyed. Compari-sons will be made between the Bessemer and open-hearth processes for the sake of clear and ready understanding,

Jan 1, 1940

By Frank Riddle

THE life of thermocouples is governed, to a large extent, by the protection they receive when in use; particularly when the temperatures being measured are high and the products of combustion are reducing in character. Several types of protection tubes are being used for this work; they are made of ordinary and aluminous porcelain, fused quartz, carborundum, fused alumina, fireclay, and some kinds of metal. All of them may render good service under certain conditions but they must be used for the purpose for which they are intended. For example, fused-quartz tubes are very good when excessive changes in temperature occur, but under certain conditions they will crystallize and lose their strength. Porcelain is used in several ways in connection with the use of thermocouples: for insulating the two wires of the couple and to. prevent short circuits; for protecting the entire couple in a refractory gas-tight tube, which is ordinarily fastened to and is considered part of a properly equipped thermocouple; and for protecting the complete thermocouple from the possibility of physical injury and to support it. This tube is made porous and strong and is ordinarily built right into the wall or crown of the furnace, as the case may be. The insulating tubes must be small and sufficiently refractory to withstand the temperatures at which they are to be used. The length of the tubes, porosity of the material from which they are made, etc. does not particularly matter. The tubes are sometimes made with two or even four holes, the latter being used where it is desirable to have two couples as close together as possible for calibration work. The thermocouple protection tube must be of proper size to permit the thermoelements and insulating tubes to be inserted or taken out easily. It must be porous enough to withstand sudden changes in temperature and yet gas-tight, as well as refractory enough to withstand the furnace temperature, even if the tube protrudes into the furnace in a horizontal position without support for a reasonable distance. If the

Jan 9, 1919

Joseph Esrey Johnson, Jr., had already achieved rare distinction as an able metallurgist, clear thinker, brilliant author, and wise consulting engineer to bankers and operators; he had achieved the essentials of a great career when dcath cut short his activities on Apr. 4, 1919, in the forty-ninth year of his age. He belonged to a family of iron blast-furnace men and mine managers. His father, Major J. E. Johnson, after serving with distinction in the Army of the North, identified himself with the iron mines and blast furnace at Longdale, Va., with which he was connected during almost his entire business life. It is significant, that, during those troublous times of reconstruction in the South, he enjoyed always the affection and respect of his neighbors and associates alike. From him his son obtained not only a thorough training in blast-furnace practice and iron mining, but great personal courage and force of character. His mother, who survives both her husband and sons, possesses rare intellectuality, humor and a tenderness and human sympathy which those who were privileged to know well J. E. Johnson, Jr., recognized beneath his exterior of aggressiveness and will power. In a recently published analysis of the qualities which characterize the world's great men, three traits stand out preeminently; viz., independence, courage, and intellectuality. Each of these characteristics J. E. Johnson, Jr., possessed in extraordinary degree. His early education was obtained under a private tutor at Longdale, and this circumstance probably enhanced a natural tendency to independence of character and individuality which, however, under the control of his unusual power of straight thinking and clear analysis never allowed him to go far astray. It has been said of him that if once he set his mind to a problem, however knotty, he scored a bull's-eye before the subject was dropped. His manner of attacking a subject involved first mastering the details of the available knowledge; then, putting this acquired information to one side, with an untrammeled mind blazing out a path of his own, so clear, so well-defined, and expressed in such simple terms that he illuminated the whole subject without distorting the original data or discussion. His two books, "Blast-furnace Construction in America" and "The Principles, Operation, and Products of the Blast Furnace, "on the iron blast furnace together form the most comprehensive, the most enlightening, and the most useful treatise on the subject ever produced in any language. But his ability did not end with the mastery and elucidation of principles enunciated by his predecessors; his own

Jan 1, 1920

By V.F. Marsters

Peru has produced petroleum since the early seventies, the first work being in the Zorritos field, in the Province of Tumbes, adjoining Ecuador. In the early nineties, the Negritos field, in the Department of Piura, came into prominence, and by 1905 had attained an annual production of 335,160 bbl. The early development of the field was under the general direction of the London & Pacific Petroleum Co., but it is now handled by the International Petroleum Co. In 1900 and 1901, the Lobitos field became the seene of marked activity. In 1905, its total production amounted to 75,000 bbl.; it has continued to increase, as has Negritos. From 1897 to 1902, there was prospecting in the region of La Brieta (or Fernandex), on the Mancora River, about 25 to 30 km. from the coast. Small production of a heavy oil was obtained from three different sands. So far as the author knows, no work has been done in that locality since 1902. There are thus four distinct fields in the north end of the Peruvian coasta1 plain. The remaining productive locality of Peru is the Pirin or Pusi field, at the northwest end of Lake Titicaca, Department of Puno, in southern Peru. The first prospecting near Pusi was done by Brown Brothers, of Los Angeles, Calif., who obtained modest production about 1906; according to reports, activities ceased about 1914 or 1915. The maximum annual production was obtained about 1908, estimated at 76,000 barrels. Peru possesses two distinct geographic provinces in which we may look for the development of a larger oil industry; namely, the coastal plain province, and the inter-Andean plains. Coastal Plain Province The coastal province is most prominently developed in the Province. of Tumbes and the Departments of Piura, and Lambayeque.l It 1 For details concerning the geology of this part of Peru, see Bol. No. 50, Cuerpo de Ingenirros de Minas "Informe preliminar sobre In Zona Petrolifera del Norte del Peru," par V. 1". Marsters.

Jan 1, 1923

By V. F. Marsters

Peru has produced petroleum since the early seventies, the first work being in the Zorritos field, in the Province of Tumbes, adjoining Ecuador. In the early nineties, the Negritos field, in the Department of Piura, came into prominence, and by 1905 had attained an annual production of 335,160 bbl. The early development of the field was under the general direction of the London & Pacific Petroleum Co., but it is now handled by the International Petroleum Co. In 1900 and 1901, the Lobitos field became the seene of marked activity. In 1905, its total production amounted to 75,000 bbl.; it has continued to increase, as has Negritos. From 1897 to 1902, there was prospecting in the region of La Brieta (or Fernandex), on the Mancora River, about 25 to 30 km. from the coast. Small production of a heavy oil was obtained from three different sands. So far as the author knows, no work has been done in that locality since 1902. There are thus four distinct fields in the north end of the Peruvian coasta1 plain. The remaining productive locality of Peru is the Pirin or Pusi field, at the northwest end of Lake Titicaca, Department of Puno, in southern Peru. The first prospecting near Pusi was done by Brown Brothers, of Los Angeles, Calif., who obtained modest production about 1906; according to reports, activities ceased about 1914 or 1915. The maximum annual production was obtained about 1908, estimated at 76,000 barrels. Peru possesses two distinct geographic provinces in which we may look for the development of a larger oil industry; namely, the coastal plain province, and the inter-Andean plains. Coastal Plain Province The coastal province is most prominently developed in the Province. of Tumbes and the Departments of Piura, and Lambayeque.l It 1 For details concerning the geology of this part of Peru, see Bol. No. 50, Cuerpo de Ingenirros de Minas "Informe preliminar sobre In Zona Petrolifera del Norte del Peru," par V. 1". Marsters.

Jan 1, 1923

L. C. Graton, Cambridge, Mass.—The subject of chalcocite occur; rence and its geological significance has, of course, a very important commercial bearing, as shown by the recent remark of a hard-headed mining .man: "This secondary enrichment business is one thing you geologists have put up which we can hang on to, and come out right." Most enrichments of copper ores depend upon the formation Of chalcocite from leaner sulphides. Recently it has been shown that not only does there exist this secondary or derived chalcocite, * but that in certain ores the mineral is present as an initial or original constituent, which therefore we may call primary. The desirability of distinguishing between these two kinds of chalcocite is evident and has recently been emphasized. That constitutes the first problem in this connection. I believe many who are working upon secondary enrichment of mineral deposits are giving much attention to that particular question. It is now possible to distinguish primary from secondary chalcocite in many cases. In such cases, what do we know of the' conditions under which this secondary or derived chalcocite was formed? , This is the second main question in connection with the subject. It is now plain, at least in many instances, that the formation of this derived chalcocite represents a phase of oxidation if we have in mind the primary ore as the thing acted upon. The next important question—and it is most important—is: does such oxidation go on above the zone where the rocks are saturated with water—that is, above the water level—or below, or indiscriminately above and below? Many of you have, or have had, opportunities to study at first hand, day after day, occurrences that' enable valuable conclusions to be drawn upon these and other important questions concerning the formation and significance of chalcocite. It is greatly to be hoped that your testimony will be made available and undoubtedly it will go far toward clearing up some of these doubtful points. John D. Irving, New Haven, Conn.—A short time before this meeting was called, H. V. Winchell, who was unable to be present, requested me to exhibit and describe these two samples of pyrite. (Exhibiting specimens.) They consist of fragments of pyrite inclosed in two small bottles. The first bottle shows fragments of pyrite which were immersed in water carrying copper sulphate but without SO2 for a period of two years. They remained comparatively clear and bright. No chalcocite has been deposited on them. The second bottle shows fragments of

Jan 1, 1915

By John Birkinbine

" Whether an iron-ore should be roasted is a question which very seldom arises ; at least, this question seldom ought to arise. With the exception of the red impalpable oxide, the whole series of ironores require roasting—even the specular iron-ore, if it is very compact—but the best oxide, if too compact, works badly in the furnace. All other ores should be subjected to calcination. Some ironmasters are in the habit of using the hydrates raw, but this should riot be done where clay-ores are smelted or where the hydrates contain either chlorides or phosphates. But in the latter case, the pig metal will be cold-short if there is too much phosphorus. Under all circumstances, however, it is best to roast the ores if we expect good metal and well-regulated furnace operations. " The object of roasting ores is to produce higher oxidation and to expel injurious admixtures. In both cases liberal access of atmospheric air is required ; we should, therefore, so arrange our roasting operations as to fulfil these conditions, from which it will appear that different ores require different treatment."* The above may be considered an extreme, and perhaps erroneous view; but there is no question as to the absence of a general appreciation concerning the value of preparing ores of iron for smelting in the blast-furnace.

Jan 1, 1884

By Leonard Larson

DURING several years immediately preceding the adoption of wet-charge smelting at McGill, various necessary conditions affecting this procedure, such as plant rearrangement and the metallurgical nature of the concentrate produced at the concentrator, were fully considered. Wet-charge smelting is not altogether novel to the recently recon-structed smelter at McGill. A number of years prior to this improve-ment, when flotation methods were initiated at the concentrator, large tonnages of wet and (at that time) sticky flotation concentrate were charged directly into the reverberatory furnaces, because of the difficulty in handling the entire tonnage in the roasters. The plant had excess reverberatory units and this surplus furnace capacity was utilized to smelt raw flotation concentrate. During the years 1927 and 1928, a number of actual operating furnace test runs were made to determine in principle the feasibility of wet-smelt-ing operation. Results were encouraging, and in November 1932 the roasting plant was shut clown. For some time thereafter the wet feed was delivered directly to the reverberatory side-charging calcine hoppers already in place. Feeding the wet material through the old calcine hoppers and charge holes into the furnace involved considerable labor, but under the conditions existing at that time it was desirable to continue wet smelting even under the handicap of this laborious procedure. The smelting plant during this period was on a curtailed production basis, operating only about 15 days per month. The alternate starting up and shutting clown of the roasting plant presented a difficult problem and charging the wet material directly to the furnace entirely eliminated this difficulty. The roasting plant was never operated thereafter.

Jan 1, 1938

By M. Muskat, H. H. Evinger

A METHOD has been developed whereby one may calculate the productivity factors of producing formations from a knowledge of the reservoir conditions. Account is taken not only of the heterogeneous character of the gas-oil flow system but also of the detailed variations with pressure of the shrinkage and viscosity of the oil, the solubility of the gas in the oil, and even the variability of the gas viscosity and the deviation of the gas from ideal behavior. Curves are shown giving the results of numerical calculations on the production rate as a function of the pressure differential for a high-pressure and a low-pressure system, three values of gas-oil ratio being treated in each case. Curves are also given showing the variation with distance from the well of the pressure, oil saturation, and permeability. The effect of connate water is briefly discussed in relation to the apparently large discrepancies between the calculated and observed productivity-factor values. INTRODUCTION The significance of the productivity factor as a measure of the capacity of an oil-bearing formation to produce is well recognized; for it is the composite and integrated resultant of the physical properties of both the porous medium and the fluid stream passing through it with respect to the ease with which the particular petroleum fluids present in the formation can flow through it and into producing wells. The most direct method of determining the productivity factor of a well consists, as is well known, in the simultaneous measurement of reservoir-pressure differentials and rates of production and the expression of the data in terms of rate of flow per unit pressure drop.1 Actual measurements carried out in this manner on producing wells have given factors that generally lie in the range of 0 to 100 bbl. per day per pound pressure drop. This wide range arises not only from variations in permeability but also from the varying sand thickness of producing formations. One of the aims of developing a theory of the mechanics of oil production obviously is that of predicting what the productivity factor should be from a knowledge of the individual characteristics of the producing formation and the fluids produced. For homogeneous fluid systems passing through a porous medium into a producing well, it has been known for some time that the steady-state rate of liquid flow Q is given by the formula:* [ ] where k is the sand permeability, h its thickness, µ the liquid viscosity, [Ap] the pressure drop between the well and the distant parts of the reservoir, in particular that at a radius [ro ]and [r ] is the well radius. This gives the productivity factor: [ ] which will have a numerical value for a liquid of I centipoise viscosity of 0.9316 or

Jan 1, 1941

By G. K. Manning, C. H. Lorig

Two metallurgical tools have acquired wide use within the past several years as a means of studying the transformation characteristics of steel. One is a technique used first by Bain and Davenport for determining the transformation characteristics of a steel at constant temperature; the second is the end-quench hardenability test. Constant-temperature transformation curves like those of Bain and Davenport have done much to rationalize the metal¬lography of steel; however, in commercial practices, constant-temperature transformation is seldom encountered, therefore only rarely can such curves be directly applied. The real reason for the determination of such curves lies, in the fact that they provide a way of thinking about transformation that is both convenient and productive. The end-quench hardenability test is a more practical means of studying transformation, for, by correlating positions on the hardenability bar with shapes of different masses, an almost direct application of the results can be made. Unfortunately, the end-quench test, though practical, can do very little toward improving the metallurgists' way of thinking about transformation. These two metallurgical tools, dealing with precisely the same phenomenon, should be very closely associated in metallurgists' minds. Actually, they are frequently pushed into separate mental corners and considered as being more or less distinct and unrelated. The reason for this is that no strong connecting link between them has been developed. An attempt is sometimes made to relate these two tools by projecting the critical cooling rate on the isothermal transformation plot as illustrated in Fig. I. The critical cooling rate is considered as a constant rate-though in practical applications, cooling rates are never constant-and this constant cooling rate is given uniform significance from the Ae temperature down to the temperature of initial transformation. A little thought indicates the errors of such a procedure. Certainly the time interval spent just below point A of Fig. I cannot be as effective in promoting nucleation as is the time interval spent just above point B. Yet the procedure represented in Fig. I considers all the time spent between temperatures A and B to be just as effective in promoting nucleation as though all the time were spent at temperature B. Furthermore, change the shape of the isothermal curve between points B and C in any way desired, and the required critical cooling rate is not changed one iota. This cannot possibly be true. Such a way of thinking about critical cooling rates not only is incapable of giving any results that are quantitatively satisfactory but is likely to give very misleading qualitative results.

Jan 1, 1946

AS you have been able to observe, I have up to the present demonstrated as, well as I knew how in writing the art of casting- and the methods of making moulds and of baking them; then the arrangements of the furnaces for melting the materials, including those made for melting by reverberation of flames or with bellows and charcoal, and the hearth, basket, ladle, and other similar instruments customary in such operations. Now I wish to show you how to bring to their conclusion the works for which these instruments are made, and show

Jan 1, 1942

By R. H. Wightman

THE following paper describes current mining practices of the Riverside Cement Co. at its Crestmore plant, Riverside, California. For a number of years the Riverside Cement Co. obtained its raw materials by surface quarry operations but after these deposits were exhausted for equipment available at that time, the company started underground mining. Mine workings were begun in 1927 to 1930 for the recovery of limestone by block-caving methods. GEOLOGY The bed of limestone that is being worked is a metamorphosed and recrystallized limestone, which is generally white in color and from medium to coarsely crystalline. This bed is fissured by water courses that vary from minute cracks to large areas. The bed has also been cracked by intrusions along the footwall and hanging wall. These walls are coarse-grained, gray, quartz granodiorite. The strike of the deposit is north and south and it dips to the east at an angle of approximately 50º. The bed is approximately 1700 ft. long, 270 ft. thick at right angles to the dip at the middle of the deposit and tapers to a thickness of approximately 100 ft. at each end. MINING METHODS The mine layout consists of four main levels with elevations as follows: 892 Collar of shaft. 800 Manway level used for ventilation, prospect purposes and as an entrance into the stopes. 700 Mining level where all material is extracted and on which are located the tapping grizzlies. This is the elevation from which all main cutoff stopes and undercutting work is started. 660 Haulage level where the limestone is drawn from transfer raises into the cars and is transported to the tipple by electric locomotives. 633 Level where all water is collected and which keeps the general water table below the working levels. A detailed description of the mine was given in U. S. Bureau of Mines Information Circular No. 6795, in June 1934. Current Block Development The first blocks to be caved were developed very much after the procedure followed in the copper mines of Arizona. This paper covers the ninth block to be caved. With a hard, tough rock like our limestone, it was found that some alterations in the development and control of draw in caving were necessary to secure better crushing effect and provide more safety for such secondary blasting as is required. Sequence of Block Development I. The fringes of the 800-ft. manway level are driven to confirm the diamond drill information and serve to determine the final location and development required for the block (Fig. I).

Jan 1, 1944

By E. Goldin, H. J. Juretschke

THE electrical properties of porous conductors have been studied ever since such materials, usually prepared by pressing and sintering of metallic powders, obtained practical importance. In most cases, however, the results have not been easy to interpret because of the great number of independent variables such as powder size, pressure, pressing rate and temperature, subsequent thermal history, porosity, and so on, which enter into the fabrication of industrially desirable materials. In recent years an interpretation of these properties has become of interest because the electrical properties of many new substances, prepared as fine powders by crystallization from the vapor phase or by reactions in the solid state at high temperatures, have to be determined on porous samples formed from the powder. Since theoretically significant information must refer to the fully dense state of the material, it is important to relate the electrical properties measured on such porous samples to those expected for a sample of 100 per cent density. A simple theory for the porosity dependence of the electrical conductivity and the Hall effect was recently proposed by Juretschke, Landauer, and Swanson.' Their model, assuming a distribution of pores of equal size and shape, sufficiently far apart so that each pore is embedded in a region of uni-

Jan 1, 1959

By Nicholas J. Grant, Ernest P. Abrahamson

IN recent work, Bloom and Grant' and Stein and IGrant' have indicated that a high temperature chromium phase exists. In the 68 pct Cr-Ni binary they found a eutectoid reaction, P chromium transforming to a chromium plus y nickel at 1215°C. Un-

Jan 1, 1957

Jan 11, 1951

By L. A. Mekler

The recirculating furnace is primarily a heating apparatus of the convection type in which the heat-absorbing surfaces are heated by a mixture of fresh products of combustion and a portion of the combustion gases that have already given off a part of their heat in their previous passage over the heat-absorbing surfaces. In its basic conception, the recirculating furnace can be considered as a closed thermal system in which the heat-absorbing surfaces are constantly swept by a fixed quantity of products of combustion at a given initial temperature with the gases being constantly returned to the furnace and reheated before they again enter the heating zone. Gases equal in amount to those produced by the fuel burned to reheat the circulating gases are constantly ejected from the system to the stack. The recirculating furnace is the most suitable apparatus for heating by convection where low furnace temperatures must be maintained and where only a small portion of the available heat is taken out of the gases, particularly where the maximum allowable furnace temperature is low and where the final temperature of the gases is only a few hundred degrees below their initial temperature. In such cases, recirculation not only provides a method of reducing the rather high combustion temperatures of the fuel when burned without a large amount of excess air, but, by returning to the furnace the heat content of the gases at their final temperature, recovers a large portion of heat that otherwise would have been lost through the stack. The convection-type oil still is particularly suitable for the application of flue-gas recirculation. In an oil still, the heating of the oil is accomplished by applying to the tube surfaces a given quantity of heat of a certain predetermined quality, usually with the initial temperature of the gases not over 1500" F. as measured by thermocouples placed above the tube bank. To obtain the full benefit of the heating surface of the coil, the final temperature of the gases, after passing over the coil, is kept 200" to 300" higher than the temperature of the incoming oil. This final temperature varies from 500" F. for a topping still with only a slight or no

Jan 1, 1928

By Christopher Haycocks, Michael Karmis, David G. Lundy

Roof bolting is the most common means of support in under- ground coal mines. The main advantages of this support system are the relative ease of installation and the ability to provide a stable and unobstructed work area. Roof bolts can be broadly classified into two categories, mechanical and resin bolts. Currently, about 20% of all bolts used are the resin types, and trends show an increasing popularity of these kinds. Although the reinforcing effects of resin bolts have been well demonstrated, there is, nevertheless, a considerable lack of knowledge of their interaction with the surrounding strata. To study this interaction and to further investigate the mechanisms involved in resin bolting, an instrumentation system was designed and tested in a southwestern Virginia coal mine. The instrumentation system was composed of straingaged resin bolts, convergence and differential sag stations, and a borescope. Strain gages mounted on the bolt determined axial, bending, and shear strain at several levels along the axis of the bolt. The roof movement, as measured by the convergence and differential sag readings and as observed by the borescope, correlated well with the strains registered on the bolts.

Jan 1, 1983

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By R. H. Olds, B. H. Sage

The transient flow of gases in long pipe lines is a problem of industrial interest. The present discussion deals with the application of the conservation of momentum and material to the transient flow of gas in conduits which are long with respect to their diameter. Solutions of the resulting equations include consideration of variations in friction and specific volume of the fluid as functions of time and position along the conduit. The changes in state along the pipe line are established as a function of time. The methods proposed may be extended to other situations. The flow of compressible fluids under steady conditions' has been considered in detail. Primary emphasis was placed on the development of simple means of taking into account the non-uniform flow' realized in long conduits under such conditions. Binder2 discussed the essential differences between the flow of compressible and uoncompressible fluids. Bonilla" proposed direct methods of solution for equations describing isothermal flow in long pipes. Similar considerations limited to steady flow have been discussed by Ruth.' Palsgrove 5 sugrested a graphical means of solving specific problems relating to the flow of gases in conduits of uniform section. Some of the basic concepts of the flow of a compressible viscous fluid in straight tubes have been described by Kuo.6 Problems of this type require knowledge of the equation of state of the fluid. In many cases it liar been convenient to assume that the fluid follows the relationship ascribed to a perfect gas. The treatment of unsteady flow of compressible fluids is less complete. This state of affairs result* from the fact that the differential equations relating pressure and flow rate with time and position for unsteady flow are nonlinear in character.' Muskat and Wyckoff presented an excellent treatment of the situation in laminar Bow where inertia forces were not of controlling importance. Somewhat earlier Hurst9 discussed the uncteady flow of fluids in petroleum reservoirs. Helhering-ton. MarRoberts. and Huntington'" established experimentally the pressure distribution and accumulative flow rate of natural gas through an unconsolidated sand. Recently Joffe11,12 conhitlcretl the specific problem of the flow of natural gas in relatively long.,. pipe lines for unsteady conditions with emphasis upon the economic feusibility of the storage of gas in such a reservoir. These discussions were based upon approximations of the partial differential equations applying to the condititons of flow. The results were descriptive of the physical situation and indirated the effertiveness of large pipe lines as cyclic storage facilities for natural gas. The advent of analog computers" has increased materially the practicality of solving nonlinear partial differential expressions. Several iterative numerical and graphical methods14,15,16 have been developed to solve nonlinear equations. However, it appears that the pair of simultaneous nonlinear partial differential equations involved in problems of this nature are not directly susceptible to solution by presently available analog computer or formal iterative numerical techniques. Nevertheless. graphical analyses afford a means of obtaining data of engineering value without special equipment. MATHEMATICAL CONSIDERATIONS Since the length of the conduit is large in comparison to the cross section in the cases to be considered, it is possible to treat the characteristics of the flow as independent of position in the cross section of the conduit. This possibility follows since the energy- connected with the velocity profile is small compared to that required to overcome the friction associated with its movement throughout the length of the line. Average values of the pressure. velocity. kinetic energy. momentum, and specific volume may he assigned to the fluid at any particular cross section. From a mathematical viewpoint this may be expressed in the following way for velocity: µ = µ(?X)..........(1) The uncertainties introduced by such assumptions usually are negligible when the ratio of length to diameter is greater than the order of 1.000. On this basis a volume element ma!. be considered to occupy the entire cross section of the conduit. Such an element is presented in Fig. 1.

Jan 1, 1951

By Richard R. Klimpel

This paper takes the liberation model recently developed by Klimpel and Austin for liberation from a binary system and reduces the over-all model form to a number of useful limiting cases. General use of the complete model form, while quite broad in utility, requires a numerical integration computer program for prediction of liberation given a specified minor component grain size distribution coupled with an optimization algorithm such as linear programming in order to back- calculate the associated grain size distribution from experimental data. In this paper, analytical solutions to the model are achieved for various assumed distributions of the minor component. These solutions are algebraic equations capable of predictive use with a hand calculator and back-calculation with very simple trial and error search procedures. The use of these special model solutions is illustrated on several sets of experimental liberation data, and the approach is shown to have practical utility.

Jan 1, 1984